J. Algorithm Comput. University of Tehran Journal of Algorithms and Computation 2476-2776 University of Tehran 129 Research Paper 3-difference cordial labeling of some cycle related graphs 3-difference cordial labeling of some cycle related graphs Ponraj R. Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627 412, India Maria Adaickalam M. Department of Mathematics, Kamarajar Government Arts College, Surandai-627859, India 01 06 2016 47 1 1 10 20 10 2015 10 03 2016 Copyright © 2016, University of Tehran. 2016 https://jac.ut.ac.ir/article_7927.html

Let G be a (p, q) graph. Let k be an integer with 2 ≤ k ≤ p and f from V (G) to the set {1, 2, . . . , k} be a map. For each edge uv, assign the label |f(u) − f(v)|. The function f is called a k-difference cordial labeling of G if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a k-difference cordial labeling is called a k-difference cordial graph. In this paper we investigate the 3-difference cordial labeling of wheel, helms, flower graph, sunflower graph, lotus inside a circle, closed helm, and double wheel.

Path cycle Wheel Star
J. Algorithm Comput. University of Tehran Journal of Algorithms and Computation 2476-2776 University of Tehran 129 Research Paper A Survey on Complexity of Integrity Parameter A Survey on Complexity of Integrity Parameter Shabankhah Mahmood University of Tehran, College of Engineering, Department of Engineering Science 01 06 2016 47 1 11 19 10 05 2015 02 03 2016 Copyright © 2016, University of Tehran. 2016 https://jac.ut.ac.ir/article_7931.html

Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including toughness, binding number, rate of disruption, neighbor-connectivity, integrity, mean integrity, edgeconnectivity vector, l-connectivity and tenacity. In this paper we discuss Integrity and its properties in vulnerability calculation. The integrity of a graph G, I(G), is defined to be min(| S | +m(G − S)) where S ⊂ V (G) and m(G − S) is the maximum order of the components of G − S. Similarly the edge-integrity of G is I′(G) := min(| S | +m(G − S)) where now S ⊆ E(G). Here and through the remaining sections, by an I-set (with respect to some prescribed graph G) we will mean a set S ⊂ V (G) for which I(G) =| S | +m(G − S). We define an I′-set similarly. In this paper we show a lower bound on the edgeintegrity of graphs and present an algorithm for its computation.

Integrity parameter toughness neighborconnectivity mean integrity edge-connectivity vector l-connectivity and tenacity
J. Algorithm Comput. University of Tehran Journal of Algorithms and Computation 2476-2776 University of Tehran 129 Research Paper On Generalized Weak Structures On Generalized Weak Structures Jamunarani R. Research Center, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628 215, Tamil Nadu, India Jeyanthi P. Research Center, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628 215, Tamil Nadu, India Noiri T. Shiokota-cho Hinagu, Yatsushiro-shi kumamoto-ken, 869-5142 Japan 02 06 2016 47 1 21 26 01 12 2015 19 05 2016 Copyright © 2016, University of Tehran. 2016 https://jac.ut.ac.ir/article_7932.html

Avila and Molina  introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α (g),π(g),σ(g) and β (g). This work is a further investigation of generalized weak structures due to Avila and Molina. Further we introduce the structures ro(g) and rc(g) and study the properties of the structures ro(g), rc(g), and also further properties of α (g),π(g),σ(g) and β (g) due to .

Generalized weak structure ro(g) rc(g) α (g) π(g) σ(g) β (g)
J. Algorithm Comput. University of Tehran Journal of Algorithms and Computation 2476-2776 University of Tehran 129 Research Paper Online Scheduling of Jobs for D-benevolent instances On Identical Machines Online Scheduling of Jobs for D-benevolent instances On Identical Machines Mohammadi I. University of Tehran, Department of Algorithms and Computation. Moazzami Dara University of Tehran, College of Engineering, Faculty of Engineering Science 01 06 2016 47 1 27 36 20 03 2015 03 03 2016 Copyright © 2016, University of Tehran. 2016 https://jac.ut.ac.ir/article_7933.html

We consider online scheduling of jobs with speci c release time on m identical machines. Each job has a weight and a size; the goal is maximizing total weight of completed jobs. At release time of a job it must immediately be scheduled on a machine or it will be rejected. It is also allowed during execution of a job to preempt it; however, it will be lost and only weight of completed jobs contribute on pro t of the algorithm. In this paper we study D-benevolent instances which is a wide and standard class and we give a new algorithm, that admits (2m + 4)-competitive ratio. It is almost half of the previous known upper bound for this problem.

Online Algorithms Scheduling Identical Machine Upper bound
J. Algorithm Comput. University of Tehran Journal of Algorithms and Computation 2476-2776 University of Tehran 129 Research Paper Mixed cycle-E-super magic decomposition of complete bipartite graphs Mixed cycle-E-super magic decomposition of complete bipartite graphs Marimuthu G. Department of Mathematics, The Madura College, Madurai -625 011, Tamilnadu, India Stalin Kumar S. Department of Mathematics, The American College, Madurai - 625 002, Tamilnadu,India 01 06 2016 47 1 37 52 20 10 2015 29 02 2016 Copyright © 2016, University of Tehran. 2016 https://jac.ut.ac.ir/article_7934.html

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) +  ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ 3, E(Hi) ∩ E(Hj) = ∅ for i ≠ j and ∪hi=1E(Hi) = E(G). In this paper, we prove that K2m,2n is mixed cycle-E-super magic decomposable where m ≥ 2, n ≥ 3, with the help of the results found in .

H-decomposable graph H-E-super magic labeling mixed cycle-E-super magic decomposable graph
J. Algorithm Comput. University of Tehran Journal of Algorithms and Computation 2476-2776 University of Tehran 129 Research Paper Heuristic and exact algorithms for Generalized Bin Covering Problem Heuristic and exact algorithms for Generalized Bin Covering Problem Jabari S. University of Tehran, Department of Algorithms and Computation. Moazzami Dara University of Tehran, College of Engineering, Faculty of Engineering Science Ghodousian A. University of Tehran, College of Engineering, Faculty of Engineering Science 19 03 2016 47 1 53 62 20 10 2015 29 02 2016 Copyright © 2016, University of Tehran. 2016 https://jac.ut.ac.ir/article_7936.html

In this paper, we study the Generalized Bin Covering problem. For this problem an exact algorithm is introduced which can nd optimal solution for small scale instances. To nd a solution near optimal for large scale instances, a heuristic algorithm has been proposed. By computational experiments, the eciency of the heuristic algorithm is assessed.

Generalized Bin Covering Problem heuristic algorithm greedy algorithm
J. Algorithm Comput. University of Tehran Journal of Algorithms and Computation 2476-2776 University of Tehran 129 Research Paper Zarankiewicz Numbers and Bipartite Ramsey Numbers Zarankiewicz Numbers and Bipartite Ramsey Numbers Collins Alex F. Rochester Institute of Technology, School of Mathematical Sciences, Rochester, NY 14623 Riasanovsky Alexander W. N. University of Pennsylvania, Department of Mathematics, Philadelphia, PA 19104, USA Wallace John C. Trinity College, Department of Mathematics, Hartford, CT 06106, USA Radziszowski Stanis law P. Rochester Institute of Technology, Department of Computer Science, Rochester, NY 14623 10 06 2016 47 1 63 78 08 02 2016 24 05 2016 Copyright © 2016, University of Tehran. 2016 https://jac.ut.ac.ir/article_7943.html

The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.In this work, we design and exploit a computational method for bounding and computing Zarankiewicz numbers. Using it, we obtain several new values and bounds on z(b; s) for 3≤s≤6. Our approach and new knowledge about z(b; s) permit us to improve some of the results on bipartite Ramsey numbers obtained by

Zarankiewicz number bipartite Ramsey number
J. Algorithm Comput. University of Tehran Journal of Algorithms and Computation 2476-2776 University of Tehran 129 Research Paper Randomized Algorithm For 3-Set Splitting Problem and it's Markovian Model Randomized Algorithm For 3-Set Splitting Problem and it's Markovian Model Heidari Mahdi Department of Algorithms and Computation, University of Tehran Golshani Ali Department of Algorithms and Computation, University of Tehran Moazzami D. University of Tehran, College of Engineering, Faculty of Enginering Science Moeini Ali University of Tehran, College of Engineering, Faculty of Enginering Science 01 04 2016 47 1 79 92 30 06 2015 30 03 2016 Copyright © 2016, University of Tehran. 2016 https://jac.ut.ac.ir/article_7944.html

In this paper we restrict every set splitting problem to the special case in which every set has just three elements. This restricted version is also NP-complete. Then, we introduce a general conversion from any set splitting problem to 3-set splitting. Then we introduce a randomize algorithm, and we use Markov chain model for run time complexity analysis of this algorithm. In the last section of this paper we introduce "Fast Split" algorithm.

NP-complete problem set splitting problem SAT problem Markov chain
J. Algorithm Comput. University of Tehran Journal of Algorithms and Computation 2476-2776 University of Tehran 129 Research Paper A Cellular Automaton Based Algorithm for Mobile Sensor Gathering A Cellular Automaton Based Algorithm for Mobile Sensor Gathering Saadatmand S. University of New South Wales, College of Engineering, Department of Computer Science, Sydney, Australia. Moazzami D. University of Tehran, College of Engineering, Faculty of Engineering Science Moeini A. University of Tehran, College of Engineering, Faculty of Engineering Science 24 03 2016 47 1 93 99 20 03 2015 03 03 2016 Copyright © 2016, University of Tehran. 2016 https://jac.ut.ac.ir/article_7947.html

In this paper we proposed a Cellular Automaton based local algorithm to solve the autonomously sensor gathering problem in Mobile Wireless Sensor Networks (MWSN). In this problem initially the connected mobile sensors deployed in the network and goal is gather all sensors into one location. The sensors decide to move only based on their local information. Cellular Automaton (CA) as dynamical systems in which space and time are discrete and rules are local, is proper candidate to simulate and analyze the problem. Using CA presents a better understanding of the problem.

Mobile Wireless Sensor Network Mobile Sensor Gathering Cellular Automata Local Algorithm
J. Algorithm Comput. University of Tehran Journal of Algorithms and Computation 2476-2776 University of Tehran 129 Research Paper A Mathematical Optimization Model for Solving Minimum Ordering Problem with Constraint Analysis and some Generalizations A Mathematical Optimization Model for Solving Minimum Ordering Problem with Constraint Analysis and some Generalizations Rezaei Samira Department of Algorithms and Computation, University of Tehran Ghodousian Amin University of Tehran, College of Engineering, Faculty of Engineering Science 01 04 2016 47 1 101 117 30 05 2015 01 03 2016 Copyright © 2016, University of Tehran. 2016 https://jac.ut.ac.ir/article_7949.html

In this paper, a mathematical method is proposed to formulate a generalized ordering problem. This model is formed as a linear optimization model in which some variables are binary. The constraints of the problem have been analyzed with the emphasis on the assessment of their importance in the formulation. On the one hand, these constraints enforce conditions on an arbitrary subgraph and then give sufficient conditions for feasibility, on the other hand, they provide a natural way to generalize the applied aspects of the model without increasing the number of the binary variables.

linear programming integer programming minimum ordering
J. Algorithm Comput. University of Tehran Journal of Algorithms and Computation 2476-2776 University of Tehran 129 Research Paper The edge tenacity of a split graph The edge tenacity of a split graph Bafandeh Mayvan Bahareh Department of Computer Engineering, Ferdowsi University of Mashhad 01 05 2016 47 1 119 125 30 06 2015 30 03 2016 Copyright © 2016, University of Tehran. 2016 https://jac.ut.ac.ir/article_7950.html

The edge tenacity Te(G) of a graph G is de ned as:Te(G) = min {[|X|+τ(G-X)]/[ω(G-X)-1]|X ⊆ E(G) and ω(G-X) > 1} where the minimum is taken over every edge-cutset X that separates G into ω(G - X) components, and by τ(G - X) we denote the order of a largest component of G. The objective of this paper is to determine this quantity for split graphs. Let G = (Z; I; E) be a noncomplete connected split graph with minimum vertex degree δ(G) we prove that if δ(G)≥|E(G)|/[|V(G)|-1]  then its edge-tenacity is |E(G)|/[|V(G)|-1] .

Vertex degree split graphs edge tenacity
J. Algorithm Comput. University of Tehran Journal of Algorithms and Computation 2476-2776 University of Tehran 129 Research Paper Minimum Tenacity of Toroidal graphs Minimum Tenacity of Toroidal graphs Doost Hosseini Hamid University of Tehran, College of Engineering, School of Civil Engineering 21 05 2016 47 1 127 135 30 04 2015 03 02 2016 Copyright © 2016, University of Tehran. 2016 https://jac.ut.ac.ir/article_7951.html

The tenacity of a graph G, T(G), is de ned by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We de ne τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connectivity κ(G). Then we show that such a bound for almost all toroidal graphs is best possible.

genus graph's connectivity toroidal graphs