On square sum graphs

K.A. CARMINA, REENA SEBASTIAN

Resumen


A (p, q)-graph G is said to be square sum, if there exists a bijection f : 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))2for every uv G E(G) is injective. In this paper we initiate a study on square sum graphs and prove that trees, unicyclic graphs, mCn,m > 1,cycle with a chord, the graph obtained by joining two copies of cycle Cn by a path Pk and the graph defined by path union of k copies of Cn, when the path Pn= P2 are square sum.

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