ON THE RAINBOW NEIGHBOURHOOD NUMBER
OF MYCIELSKI TYPE GRAPHS
N.K. Sudev1, C. Susanth2, S.J. Kalayathankal3
1Department of Mathematics
CHRIST (Deemed to be University)
Bengaluru - 560029, INDIA
2 Department of Mathematics
Vidya Academy of Science & Technology
Thalakkottukara, Thrissur - 680501, INDIA
3 Department of Mathematics
Kuriakose Elias College
Mannanam, Kottayam - 686561, INDIA

Abstract

A rainbow neighbourhood of a graph $G$ is the closed neighbourhood $N[v]$ of a vertex $v \in V(G)$ which contains at least one colored vertex of each color in the chromatic coloring $\mathcal C$ of $G$. Let $G$ be a graph with a chromatic coloring $\mathcal C$ defined on it. The number of vertices in $G$ yielding rainbow neighbourhoods is called the rainbow neighbourhood number of the graph $G$, denoted by $r_\chi(G)$. In this paper, we discuss the rainbow neighbourhood number of the Mycielski type graphs of graphs.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 6
Year: 2018

DOI: 10.12732/ijam.v31i6.8

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