Rainbow Vertex Coloring for Line, Middle, Central, Total Graph of Comb Graph

Abstract

Objectives: To find the rainbow vertex connection number for Line, Central, Middle and Total graphs of Comb Graph. Methods/Statistical Analysis: The methods to find the rainbow vertex connection number of any graph G is quite different from other coloring problems. Findings: The rainbow vertex connection number for line graph and middle graph of comb graph      2 n is rainbow vertex connection number for Central graph of Comb graph is 2 and Total graph of Comb graph is     3 n if n=7, 11; is     3 n -1 if n=4k+11, k ≥ 1. While finding the achromatic number for any graph G , noting that no two adjacent vertices receives same color but in the case of rainbow vertex coloring we can assign same color to the adjacent vertices. Application/Improvements: The applications of rainbow vertex connection number are same as rainbow connection number.