Theta Graph Designs
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2017
06
49
1
No
2017-06-01
Anthony D. Forbes,Terry S. Griggs,Tamsin J. Forbes
Department of Mathematics and Statistics, The Open University, Milton Keynes MK7 6AA, UK.,Department of Mathematics and Statistics, The Open University, Milton Keynes MK7 6AA, UK.,22 St Albans Road, Kingston upon Thames KT2 5HQ, UK.
1
Graph design,Graph decomposition,Theta graph
We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges.
http://jac.ut.ac.ir/article_390_49.html
http://jac.ut.ac.ir/pdf_390_02ff7ac4ba7b699fc76d94f5ad8f1549.html
Remainder Cordial Labeling of Graphs
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2017
06
49
1
No
2017-06-01
R. Ponraj,K. Annathurai,R. Kala
Department of Mathematics, Sri Paramakalyani College, Alwarkurichi-627 412, India,Department of Mathematics, Thiruvalluvar College, Papanasam-627 425, India,Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli-627 012, India
17
vertex equitable labeling,vertex Path,cycle,star,bistar,crown,comb,wheel,complete bipartite graph,complete graph graph
In this paper we introduce remainder cordial labeling of graphs. Let G be a (p, q) graph. Let f : V (G)→ {1, 2, ..., p} be a 1-1 map. For each edge uv assign the label r where r is the remainder when f(u) is divided by f(v) or f(v) is divided by f(u) according as f(u) ≥ f(v) or f(v) ≥ f(u). The function f is called a remainder cordial labeling of G if |ef (0) - ef (1)| ≤ 1 where ef(0) and ef(1) respectively denote the number of edges labeled with even integers and odd integers. A graph G with a remainder cordial labeling is called a remainder cordial graph. We investigate the remainder cordial behavior of path, cycle, star, bistar, crown, comb, wheel, complete bipartite K2,n graph. Finally we propose a conjecture on complete graph Kn.
http://jac.ut.ac.ir/article_391_49.html
http://jac.ut.ac.ir/pdf_391_f03b411b6ca5cd87d187834b590839af.html