Mean Sum Square Prime Labeling of Some Snake Graphs

Abstract

Mean  sum square prime labeling of a graph is the labeling of the vertices with {0,1,2---,p-1} and the edges with mean  of the square of the sum of the labels of the incident vertices or mean of the square of the sum of the labels of the incident vertices and one, depending on the  sum is even or odd. The greatest common incidence number of a vertex (gcin) of degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of degree greater than one is one, then the graph admits mean sum square prime labeling. Here we identify some snake graphs for mean sum square prime labeling.