Totally magic cordial labeling of some graphs
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2015
09
46
1
No
2015-09-01
P. Jeyanthi,N. Angel Benseera
2Research Center, Department of Mathematics, Aditanar College for women, Tiruchendur - 628 216, India,Department of Mathematics, Sri enakshi Government Arts College for Women (Autonomous), Madurai - 625 002, India.
1
Cordial labeling,Totally magic cordial labeling
A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + f(b) + f(ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. In this paper, we give a necessary condition for an odd graph to be not totally magic cordial and also prove that some families of graphs admit totally magic cordial labeling.
http://jac.ut.ac.ir/article_355_43.html
http://jac.ut.ac.ir/pdf_355_5e2b6a274667fa1b3976387dd2ecb005.html
All Ramsey (2K2,C4)−Minimal Graphs
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2015
11
46
1
No
2015-11-25
Kristiana Wijaya,Lyra Yulianti,Edy Tri Baskoro,Hilda Assiyatun,Djoko Suprijanto
Combinatorial Mathematics Research Group, Faculty of Mathematics and natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung 40132 Indonesia,Department of Mathematics, Faculty of Mathematics and Natural Sciences, Andalas University, Kampus UNAND Limau Manis Padang 25136 Indonesia,Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung 40132 Indonesia,Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung 40132 Indonesia,Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10 Bandung 40132 Indonesia
9
Ramsey minimal graph,edge coloring,graph 2K2,cycle graph
Let F, G and H be non-empty graphs. The notation F → (G,H) means that if any edge of F is colored by red or blue, then either the red subgraph of F con- tains a graph G or the blue subgraph of F contains a graph H. A graph F (without isolated vertices) is called a Ramsey (G,H)−minimal if F → (G,H) and for every e ∈ E(F), (F − e) 9 (G,H). The set of all Ramsey (G,H)−minimal graphs is denoted by R(G,H). In this paper, we characterize all graphs which are in R(2K2,C4).
http://jac.ut.ac.ir/article_356_43.html
http://jac.ut.ac.ir/pdf_356_651e3bc41b32f240cb33e7a9669c32df.html
Vertex Equitable Labeling of Double Alternate Snake Graphs
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
01
46
1
No
2016-01-07
P. Jeyanthi,A. Maheswari,M. Vijayalakshmi
1Research Center, Department of Mathematics, Govindammal Aditanar College for women, Tiruchendur - 628 215, Tamilnadu,India,2Department of Mathematics, Kamaraj College of Engineering and Technology, Virudhunagar, India,3Department of Mathematics, Dr.G.U. Pope College of Engineering, Sawyerpuram, Thoothukudi District, Tamilnadu, India
27
vertex equitable labeling,vertex equitable graph,double alternate triangular snake,double alternate quadrilateral snake
Let G be a graph with p vertices and q edges and A = {0, 1, 2, . . . , [q/2]}. A vertex labeling f : V (G) → A induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. For a ∈ A, let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, |vf (a) − vf (b)| ≤ 1 and the induced edge labels are 1, 2, 3, . . . , q. In this paper, we prove that DA(Tn)⊙K1, DA(Tn)⊙2K1(DA(Tn) denote double alternate triangular snake) and DA(Qn) ⊙ K1, DA(Qn) ⊙ 2K1(DA(Qn) denote double alternate quadrilateral snake) are vertex equitable graphs.
http://jac.ut.ac.ir/article_357_43.html
http://jac.ut.ac.ir/pdf_357_76d1a6298f68c081c967627653edc287.html
Mixed cycle-E-super magic decomposition of complete bipartite graphs
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016
03
46
1
No
2016-03-18
G. Marimuthu,S. Stalin Kumar
Department of Mathematics, The Madura College, Madurai -625 011, Tamilnadu, India,Department of Mathematics, The American College, Madurai -625 002, Tamilnadu,India
35
H-decomposable graph,H-E-super magic labeling,mixed cycle-E-super magic decomposable graph
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, ∑νεV (H) f(v) + ∑νεE (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 [1].
http://jac.ut.ac.ir/article_358_43.html
http://jac.ut.ac.ir/pdf_358_c5cc97b6cfd026d4c13e87b580a03b9a.html
Toughness of the Networks with Maximum Connectivity
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2015
09
46
1
No
2015-09-01
D. Moazzami
University of Tehran, College of Engineering, Department of Engineering Science
51
toughness,Harary graph,maximum connectivity,Network
The stability of a communication network composed of processing nodes and communication links is of prime importance to network designers. As the network begins losing links or nodes, eventually there is a loss in its effectiveness. Thus, communication networks must be constructed to be as stable as possible, not only with respect to the initial disruption, but also with respect to the possible reconstruction of the network. For any fixed integers n,p with p ≥ n + 1, Harary constructed classes of graphs Hn,p that are n-connected with the minimum number of edges. Thus Harary graphs are examples of graphs with maximum connectivity. This property makes them useful to network designers and thus it is of interest to study the behavior of other stability parameters for the Harary graphs. In this paper we study the toughness of the third case of the Harary graphs.
http://jac.ut.ac.ir/article_359_43.html
http://jac.ut.ac.ir/pdf_359_c2bbe11d39cad5af84f5731fc7c50217.html
Further results on total mean cordial labeling of graphs
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2015
09
46
1
No
2015-09-01
R. Ponraj,S. Sathish Narayanan
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627 412, India,Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627 412, India
73
cycle,path,union of graphs,star,ladder
A graph G = (V,E) with p vertices and q edges is said to be a total mean cordial graph if there exists a function f : V (G) → {0, 1, 2} such that f(xy) = [(f(x)+f(y))/2] where x, y ∈ V (G), xy ∈ E(G), and the total number of 0, 1 and 2 are balanced. That is |evf (i) − evf (j)| ≤ 1, i, j ∈ {0, 1, 2} where evf (x) denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). In this paper, we investigate the total mean cordial labeling of Cn2, ladder Ln, book Bm and some more graphs.
http://jac.ut.ac.ir/article_360_43.html
http://jac.ut.ac.ir/pdf_360_9d2173db725a3759d46d6f1e33486b61.html