On adjacent vertex distinguishing total coloring of quadrilateral snake

Abstract

In this paper, we prove the existence of the adjacent vertex distinguishing total coloringnof quadrilateral snake, double quadrilateral snake, alternate quadrilateral snake and double alternate quadrilateral snake in detail. Also, we present an algorithm to obtain the adjacent vertex distinguishing total coloring of these quadrilateral graph family. The minimum number of colors required to give an adjacent vertex distinguishing total coloring (abbreviated as AVDTC) to the graph G is denoted by avt(G).