## SOME RESULTS ON VERTEX-EDGE NEIGHBORHOOD PRIME LABELING

## SOME RESULTS ON VERTEX-EDGE NEIGHBORHOOD PRIME LABELING

*N. P. Shrimali, A. K. Rathod*

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## Abstract

Let G be a graph with vertex set V (G) and edge set E(G). For u 2 V (G), NV (u) = fw 2 V (G)juw 2 E(G)g and NE(u) = fe 2 E(G)je = uv; for some v 2 V (G)g. A bijective function f : V (G) [ E(G) ! f1; 2; 3; : : : ; jV (G) [ E(G)jg is said to be a vertex-edge neighborhood prime labeling, if for u 2 V (G) with deg(u) = 1; gcd ff(w); f(uw)jw 2 NV (u)g = 1 ; for u 2 V (G) with deg(u) > 1, gcd ff(w)jw 2 NV (u)g = 1 and gcd ff(e)je 2 NE(u)g = 1. A graph which admits vertex-edge neighborhood prime labeling is called a vertex-edge neighborhood prime graph. In this paper we investi- gate vertex-edge neighborhood prime labeling for generalized web graph, generalized web graph without central vertex, splitting graph of path, splitting graph of star, graph obtained by switching of a vertex in path, graph obtained by switching of a vertex in cycle, middle graph of path.

## Keywords

Neighborhood-prime labeling, vertex-edge neighborhood prime labeling.