abstract
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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. ¿
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 ¿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 ¿3c (G). © 2024 The Authors.