|
Eurasian Mathematical Journal, 2015, Volume 6, Number 4, Pages 77–91
(Mi emj211)
|
|
|
|
This article is cited in 1 scientific paper (total in 1 paper)
Open neighbourhood colouring of some path related graphs
N. N. Swamya, B. Sooryanarayanab a Department of Mathematics, University College of Science,
Tumkur University, Tumakuru, Karnataka 572103, India
b Department of Mathematical and Computational Studies, Dr. Ambedkar Institute of Technology, Bengaluru, Karnataka 560056, India
Abstract:
An open neighbourhood $k$-colouring of a simple connected undirected graph $G(V,E)$ is a $k$-colouring $c : V\to \{1,2,\dots,k\}$, such that, for every $w \in V$ and for all $u,v \in N(w)$, $c(u) \ne c(v)$. The minimal value of $k$ for which $G$ admits an open neighbourhood $k$-colouring is called the open neighbourhood chromatic number of $G$ and is denoted by $\chi_{onc} (G)$. In this paper, we obtain the open neighbourhood chromatic number of the line graph and total graph of a path $P_n$. We also obtain the open neighbourhood chromatic number of two families of graphs which are derived from a path $P_n$, namely $k^{th}$ power of a path and transformation graph of a path.
Keywords and phrases:
colouring, chromatic number, open neighbourhood, power graph, transformation graph.
Received: 08.01.2015
Citation:
N. N. Swamy, B. Sooryanarayana, “Open neighbourhood colouring of some path related graphs”, Eurasian Math. J., 6:4 (2015), 77–91
Linking options:
https://www.mathnet.ru/eng/emj211 https://www.mathnet.ru/eng/emj/v6/i4/p77
|
Statistics & downloads: |
Abstract page: | 197 | Full-text PDF : | 94 | References: | 28 |
|