Sum divisor cordial labeling for path and cycle related graphs

Abstract

A sum divisor cordial labeling of a graph GG with vertex set VV is a bijection ff from VV to {1,2,⋅⋅⋅,|V(G)|}{1,2,···,|V(G)|} such that an edge uvuv is assigned the label 1 if 2 divides f(u)+f(v)f(u)+f(v) and 00 otherwise; and the number of edges labeled with 00 and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we prove that P2n,Pn⊙mK1,S(Pn⊙mK1),D2(Pn),T(Pn)Pn2,Pn⊙mK1,S(Pn⊙mK1),D2(Pn),T(Pn), the graph obtained by duplication of each vertex of path by an edge, T(Cn),D2(Cn)T(Cn),D2(Cn), the graph obtained by duplication of each vertex of cycle by an edge, C^{(t)}_{4}, book, quadrilateral snake and alternate triangular snake are sum divisor cordial graphs.