Acyclic 3-coloring of generalized Petersen graphs

Abstract

An acyclic k-coloring of a graph G is a k-coloring of its vertices such that no cycle of G is bichromatic. G is called acyclically k-colorable if it admits an acyclic k-coloring. In this paper, we prove that the generalized Petersen graph P(n, k) is acyclically 3-colorable except P(4, 1) and the classical Petersen graph P(5, 2).

Radio Number for Generalized Petersen Graphs $P(n,2)$

“…Very few graphs have been proved to have RL and achieve the radio number. In this paper, we have investigated the values of radio number for Peterson graphs [28]- [30]. Graph labeling has many applications in coding theory, x-ray crystallography, radar, astronomy, circuit design, communication network addressing, data base management.…”

Weakly convex and convex domination numbers for generalized Petersen and flower snark graphs

“…In the recently published literature, various properties of GP (n, k) have been investigated: minimum span of L(2, 1)-labeling [1], minimum vertex cover [4], metric dimension [2,27], strong metric dimension [18], decycling number [13], component connectivity [10], acyclic 3-coloring [34], crossing numbers [25], independence number [11], and others. Some recent works dealing with variants of the domination numbers in the generalized Petersen graphs are: domination number [3,12,26], domatic number, total domatic number, and k-ply domatic number [33], efficient domination number [17], power domination number [32], 2-rainbow domination [5,31], and others.…”