eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2017-06-01
49
1
1
16
390
Theta Graph Designs
Anthony D. Forbes
anthony.d.forbes@gmail.com
1
Terry S. Griggs
terry.griggs@open.ac.uk
2
Tamsin J. Forbes
tamsin.forbes@gmail.com
3
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.
We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges.
http://jac.ut.ac.ir/pdf_390_02ff7ac4ba7b699fc76d94f5ad8f1549.html
Graph design
Graph decomposition
Theta graph
eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2017-06-01
49
1
17
30
391
Remainder Cordial Labeling of Graphs
R. Ponraj
ponrajmaths@gmail.com
1
K. Annathurai
kannathuraitvcmaths@gmail.com
2
R. Kala
karthipyi91@yahoo.co.in
3
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
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/pdf_391_f03b411b6ca5cd87d187834b590839af.html
vertex equitable labeling
vertex Path
cycle
star
bistar
crown
comb
wheel
complete bipartite graph
complete graph graph