Deciding Graph non-Hamiltonicity via a Closure Algorithm
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
11
48
1
No
2016-11-28
E. R. Swart,Stephen J. Gismondi,N. R. Swart,C. E. Bell,A. Lee
Kelowna, British Columbia, Canada,University of Guelph, Canada,University of British Columbia Okanagan, Canada,Guelph, Ontario, Canada,University of Guelph, Canada
1
Hamilton cycle,decision problem
We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the n! Hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices P, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. A graph instance (G) is initially coded as exclusion set E, whose members are pairs of components of P, {pu,i, pv,i+1}, i = 1, n - 1, for each arc (u, v) not in
http://jac.ut.ac.ir/article_371_47.html
http://jac.ut.ac.ir/pdf_371_15545482e67a30452c97e86eb5b51fa9.html
On the tenacity of cycle permutation graph
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
12
48
1
No
2016-12-08
D. Jelodar,D. Moazzami,P. Nasehpour
University of Tehran, Department of Algorithms and Computation,University of Tehran, College of Engineering, Department of Engineering Science,University of Tehran, College of Engineering, Department of Engineering Science
37
tenacity,Tenacious,Cycle Permutation,toughness,integrity
A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.
http://jac.ut.ac.ir/article_372_47.html
http://jac.ut.ac.ir/pdf_372_a7b34f56efc535ed46a94f44aa7e3d23.html
A note on 3-Prime cordial graphs
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
11
48
1
No
2016-11-10
R. Ponraj,Rajpal Singh,S. Sathish Narayanan
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627412, India,Research Scholar, Department of Mathematics Manonmaniam Sundaranar University, Tirunelveli-627012, India,Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627412, India
45
path,union of graphs
Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate 3- prime cordial labeling behavior of union of a 3-prime cordial graph and a path Pn.
http://jac.ut.ac.ir/article_373_47.html
http://jac.ut.ac.ir/pdf_373_495c61efe2289c038edc6c7099386507.html
Edge pair sum labeling of some cycle related graphs
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
11
48
1
No
2016-11-01
P. Jeyanthi,T. Saratha Devi
Govindammal Aditanar College for Women Tiruchendur-628 215, Tamil Nadu, India,Department of Mathematics, G.Venkataswamy Naidu College, Kovilpatti-628502,Tamilnadu,India.
57
Edge pair sum labeling,edge pair sum graph,double triangular snake,wheel graph,ower graph
Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: V (G) → Z - {0} defined by f*(v) = ΣP∈Ev f (e) is one-one where Ev denotes the set of edges in G that are incident with a vertex v and f*(V (G)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} U {±k(p+1)/2} according as p is even or odd. A graph with an edge pair sum labeling is called an edge pair sum graph. In this paper we prove that the graphs GL(n), double triangular snake D(Tn), Wn, Fln, and admit edge pair sum labeling.
http://jac.ut.ac.ir/article_374_47.html
http://jac.ut.ac.ir/pdf_374_56568b68b988fc59429af15e748b7a64.html
4-Prime cordiality of some classes of graphs
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
12
48
1
No
2016-12-15
R. Ponraj,Rajpal Singh,S. Sathish Narayanan,A. M. S. Ramasamy
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627 412, India,Research Scholar, Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli-627012, India,Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627 412, India,Department of Mathematics, Vel Tech Dr.R.R & Dr.S.R Technical University, Chennai-600002, India
69
Complete graph,wheel,path,book,flower
Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate 4- prime cordial labeling behavior of complete graph, book, flower, mCn and some more graphs.
http://jac.ut.ac.ir/article_375_47.html
http://jac.ut.ac.ir/pdf_375_01050790c89557f0425ee26385c3b6b9.html
Further results on odd mean labeling of some subdivision graphs
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
12
48
1
No
2016-12-16
R. Vasuki,S. Suganthi,G. Pooranam
Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215, Tamil Nadu, India,Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215, Tamil Nadu, India,Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215, Tamil Nadu, India
81
labeling,odd mean labeling,odd mean graph
Let G(V,E) be a graph with p vertices and q edges. A graph G is said to have an odd mean labeling if there exists a function f : V (G) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : E(G) → {1, 3, 5,...,2q - 1} defined by
f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd
is a bijection. A graph that admits an odd mean labeling is called an odd mean graph. In this paper, we have studied an odd meanness property of the subdivision of the slanting ladder SLn for all n ≥ 2; Cn Θ K1 for n ≥ 3; the grid Pm × Pn for m, n ≥ 2; Cm@Cn for m, n ≥ 3 and P2m Θ nK1 for all m, n ≥ 1..
http://jac.ut.ac.ir/article_376_47.html
http://jac.ut.ac.ir/pdf_376_b5919c4f284019e6cc358136ade4b8ed.html
An Optimization Model for Epidemic Mitigation and Some Theoretical and Applied Generalizations
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
11
48
1
No
2016-11-01
Sima Ranjbarfard,Amin Ghodousian,D. Moazzami
Department of Algorithms and Computation, University of Tehran.,University of Tehran, College of Engineering, Faculty of Engineering Science,University of Tehran, College of Engineering, Faculty of Engineering Science
99
Epidemic control,Networks,Link removal,Quarantine,Partitioning,Optimization
In this paper, we present a binary-linear optimization model to prevent the spread of an infectious disease in a community. The model is based on the remotion of some connections in a contact network in order to separate infected nodes from the others. By using this model we nd an exact optimal solution and determine not only the minimum number of deleted links but also their exact positions. The formulation of the model is insensitive to the number of edges in a graph and can be used (with complete or local information) to measure the resistance of a network before and after an infectious spreads. Also, we propose some related models as generalizations: quarantining problem including resource constraints (time, budget, etc.), maximum rescued nodes-minimum deleted links problem and minimum removed links problem nding a prespecied number of nodes with weakest connections.
http://jac.ut.ac.ir/article_379_47.html
http://jac.ut.ac.ir/pdf_379_d579d657e55fe3023b8855e49200e683.html
Constructing Graceful Graphs with Caterpillars
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
12
48
1
No
2016-12-25
Christian Barrientos,Sarah Minion
Department of Mathematics, Clayton State University, Morrow, Georgia 30260, USA,Department of Mathematics, Clayton State University, Morrow, Georgia 30260, USA
117
graceful labeling,caterpillar,graceful trees
A graceful labeling of a graph G of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of G, such that when each edge of G has assigned a weight, given by the absolute dierence of the labels of its end vertices, the set of weights is {1, 2,..., n}. If a graceful labeling f of a bipartite graph G assigns the smaller labels to one of the two stable sets of G, then f is called an -labeling and G is said to be an α-graph. A tree is a caterpillar if the deletion of all its leaves results in a path. In this work we study graceful labelings of the disjoint union of a cycle and a caterpillar. We present necessary conditions for this union to be graceful and, in the case where the cycle has even size, to be an α-graph. In addition, we present a new family of graceful trees constructed using α-labeled caterpillars.
http://jac.ut.ac.ir/article_380_47.html
http://jac.ut.ac.ir/pdf_380_ab86e4c77cafca0ee7fc0724a85925bb.html
Total vertex irregularity strength of corona product of some graphs
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
12
48
1
No
2016-12-25
P. Jeyanthi,A. Sudha
Research Centre, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628 215, Tamil Nadu, India.,Department of Mathematics, Wavoo Wajeeha Women’s College of Arts and Science, Kayalpatnam -628 204,Tamil Nadu, India.
127
irregularity strength,total vertex irregularity strength,vertex irregular total labeling,corona product of path and cycle,path and complete graph,ladder and complete graph,graph
A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the total vertex irregularity strength for n ≥ 3, m ≥ 2, Pn ⊙ K1, Pn ⊙ K2, Cn ⊙ K2, Ln ⊙ K1, CLn ⊙ K1, P2 ⊙ Cn, Pn ⊙ Km, Cn ⊙ Km
http://jac.ut.ac.ir/article_382_47.html
http://jac.ut.ac.ir/pdf_382_75d3525b3126762d9d4dfccb440cd4e7.html
A Survey on Stability Measure of Networks
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
12
48
1
No
2016-12-25
Peyman Nasehpour
Department of Algorithms and Computation, Faculty of Engineering Science, University of Tehran
141
binding number,connectivity,toughness,tenacity
In this paper we discuss about tenacity and its properties in stability calculation. We indicate relationships between tenacity and connectivity, tenacity and binding number, tenacity and toughness. We also give good lower and upper bounds for tenacity.
http://jac.ut.ac.ir/article_386_47.html
http://jac.ut.ac.ir/pdf_386_59e5788244594db95055102f8978fe03.html
Towards a measure of vulnerability, tenacity of a Graph
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
12
48
1
No
2016-12-11
Dara Moazzami
University of Tehran, College of Engineering, Department of Engineering Science
149
connectivity,integrity,toughness,binding number and tenacity
If we think of the graph as modeling a network, the vulnerability measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including connectivity, integrity, toughness, binding number and tenacity.In this paper we discuss tenacity and its properties in vulnerability calculation.
http://jac.ut.ac.ir/article_387_47.html
http://jac.ut.ac.ir/pdf_387_7999d7a1346227c73a4872acc73ba654.html
A Survey On the Vulnerability Parameters of Networks
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
12
48
1
No
2016-12-25
Mahmood Shabankhah
University of Tehran, College of Engineering, Faculty of Engineering Science
155
vulnerability measures,connectivity,binding number,toughness,integrity,tenacity
The analysis of vulnerability in networks generally involves some questions about how the underlying graph is connected. One is naturally interested in studying the types of disruption in the network that maybe caused by failures of certain links or nodes. In terms of a graph, the concept of connectedness is used in dierent forms to study many of the measures of vulnerability. When certain vertices or edges of a connected graph are deleted, one wants to know whether the remaining graph is still connected, and if so, what its vertex - or edge - connectivity is. If on the other hand, the graph is disconnected, the determination of the number of its components or their orders is useful. Our purpose here is to describe and analyze the current status of the vulnerability measures, identify its more interesting variants, and suggesta most suitable measure of vulnerability.
http://jac.ut.ac.ir/article_389_47.html
http://jac.ut.ac.ir/pdf_389_90bffa8a1a1619f646beb2bd9af65d54.html