Abstract

Let G be a graph is said to be a square sum labeling if there exist a bijectionf∶V(G)→{0,1,2,…,p-1} such that the induced function f^* ∶E(G)→N given by f^* (uv)=〖[f(u)]〗^2+〖[f(v)]〗^2, for every uv∈E(G) are all distinct. A graph which admits square sum labeling is called a square sum graph. In this paper we investigate square sum labeling for some graphs related to lilly graph. We discuss square sum labeling in the context of some graph operations namely duplication, fusion, switching in the lilly graph I_n. We prove that the duplication of an apex vertex and other vertex of lilly graph are square sum graph. We prove that the identifying any vertex of lilly graph are square sum graph. We prove that the switching of an apex vertex and other vertex of lilly graph are square sum graph and also apply coloring of the graph operations of the lilly graph is satisfying coloring condition.

Keyword

Square sum labeling, Square sum graph, Lilly graph, Duplication, Fusion, Switching, coloring.

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