Equitable coloring on subdivision vertex join of cycle Cm with path Pn

K. Praveena, M. Venkatachalam and A. Rohini
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 2, Pages 190—198
DOI: 10.7546/nntdm.2019.25.2.190-198
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Authors and affiliations

K. Praveena
Department of Computer Science,
Dr. G. R. Damodaran College of Science (Autonomous)
Coimbatore – 641 014, Tamil Nadu, India

M. Venkatachalam
PG and Research Department of Mathematics,
Kongunadu Arts and Science College (Autonomous)
Coimbatore – 641 029, Tamil Nadu, India

A. Rohini
PG and Research Department of Mathematics,
Kongunadu Arts and Science College (Autonomous)
Coimbatore – 641 029, Tamil Nadu, India

Abstract

Graph coloring is one of the research areas that shaped the graph theory as we know it today. An equitable coloring of a graph G is a proper coloring of the vertices of G such that color classes differ in size by at most one. The subdivision graph S(G) of a graph G is the graph obtained by inserting a new vertex into every edge of G. Let G1 and G2 be two graphs with vertex sets V(G1) and V(G2), respectively. The subdivision-vertex join of two vertex disjoint graphs G1 and G2 is the graph obtained from S(G1) and G2 by joining each vertex of V(G1) with every vertex of V(G2). In this paper, we find the equitable chromatic number of subdivision vertex join of cycle graph with path graph.

Keywords

  • Equitable coloring
  • Subdivision graph
  • Subdivision vertex join

2010 Mathematics Subject Classification

  • 05C15

References

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Cite this paper

APA

Praveena, K., Venkatachalam, M. (2019). Equitable coloring on subdivision vertex join of cycle Cm with path Pn. Notes on Number Theory and Discrete Mathematics, 25(2), 190-198, doi: 10.7546/nntdm.2019.25.2.190-198.

Chicago

Praveena, K., M. Venkatachalam and A. Rohini. “Equitable coloring on subdivision vertex join of cycle Cm with path Pn.” Notes on Number Theory and Discrete Mathematics 25, no. 2 (2019): 190-198, doi: 10.7546/nntdm.2019.25.2.190-198.

MLA

Praveena, K., M. Venkatachalam and A. Rohini. “Equitable coloring on subdivision vertex join of cycle Cm with path Pn.” Notes on Number Theory and Discrete Mathematics 25.2 (2019): 190-198. Print, doi: 10.7546/nntdm.2019.25.2.190-198.

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