ABSTRACT
Let G=(V,E) be a graph with p vertices and q edges. A second order triangular graceful labeling of a graph G is an one to one function π:π(πΊ)β{0,1,2,β¦,π΅π} where π΅π is the πth second order triangular number, ie., π΅π=1/6π(π+1)(2π+1), that induces a bijection πβ:E(G)β{π΅1,π΅2,β¦,π΅π} of the edges of G defined by πβ(π’π£) =|π(π’)βπ(π£)| β e=uv βE(G). A graph which admits such labeling is called a second order triangular graceful graph. In this paper, we introduce second order triangular graceful labeling and we prove that star, subdivision of star, nπΎ1,3, nπΎ2, bistar, path, comb, coconut tree, shrub and Y-tree are second order triangular graceful graphs.
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