2017
49
1
0
0
Theta Graph Designs
2
2
We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges.
1

1
16


Anthony D.
Forbes
Department of Mathematics and Statistics, The Open University, Milton Keynes MK7 6AA, UK.
Department of Mathematics and Statistics,
Iran
anthony.d.forbes@gmail.com


Terry S.
Griggs
Department of Mathematics and Statistics, The Open University, Milton Keynes MK7 6AA, UK.
Department of Mathematics and Statistics,
Iran
terry.griggs@open.ac.uk


Tamsin J.
Forbes
22 St Albans Road, Kingston upon Thames KT2 5HQ, UK.
22 St Albans Road, Kingston upon Thames KT2
Iran
tamsin.forbes@gmail.com
Graph design
Graph decomposition
Theta graph
Remainder Cordial Labeling of Graphs
2
2
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 11 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.
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17
30


R.
Ponraj
Department of Mathematics, Sri Paramakalyani College, Alwarkurichi627 412, India
Department of Mathematics, Sri Paramakalyani
Iran
ponrajmaths@gmail.com


K.
Annathurai
Department of Mathematics, Thiruvalluvar College, Papanasam627 425, India
Department of Mathematics, Thiruvalluvar
Iran
kannathuraitvcmaths@gmail.com


R.
Kala
Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli627 012, India
Department of Mathematics, Manonmaniam Sundaranar
Iran
karthipyi91@yahoo.co.in
vertex equitable labeling
vertex Path
cycle
star
bistar
crown
comb
wheel
complete bipartite graph
complete graph graph