Further Results on the 3-Consecutive Vertex Coloring Number of Certain Graphs

Abstract

A 3-consecutive vertex coloring is an assignment of colors on vertices of a graph G such that for any 3-consecutive vertices $a, b$ and c, the color of b is the same as the color of a or c. $\psi _{3c}(G)$ denotes the maximum number of colors that can be used to 3-consecutive vertex color a graph G. The main aim of this article is to give the value of $\psi _{3c}(G)$ for some particular types of graphs, which includes: necklace graphs; the Cartesian product of two paths, a cycle and a path, and two cycles; the corona product of a path and a clique; Mobius Ladder graphs; the 3rd edge line graph; triangular snake graphs, double triangular snake graphs, triple triangular snake graphs, quadrilateral snake graphs and the alternative versions of them; Hanoi graphs; Sun graphs; Barbel graphs; the n-pan graph. The objective of this article is to explore some important results on $\psi _{3c}(G)$ .

Keywords

• 3-consecutive vertex coloring
• 3-consecutive vertex coloring number
• corona product
• necklace graphs
• snake graphs