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 cycle related graphs for mean sum square prime labeling.
Highlights
All graphs in this paper are simple, finite and undirected
In [5], we introduced the concept of sum square prime labeling and proved the result for some cycle related graphs
In this paper we introduced mean sum square prime labeling using the concept greatest common incidence number of a vertex
Summary
All graphs in this paper are simple, finite and undirected. The symbol V(G) and E(G) denotes the vertex set and edge set of a graph G. In [5], we introduced the concept of sum square prime labeling and proved the result for some cycle related graphs. In this paper we introduced mean sum square prime labeling using the concept greatest common incidence number of a vertex. We proved that some cycle related graphs admit mean sum square prime labeling.
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