• PATH RELATED ARITHMETIC GRAPHS

Abstract

A (p, q) graph G = (V, E ) is said to be (k,d) arithmetic, where k and d are positive integers if its p vertices admits a labeling of distinct non negative integers such that the values of the edges obtained as the sum of the labels of their end vertices form the set{ k, k+d, …,k+ (q-1)d}. In this paper we prove that〖 P〗_n^2, 〖(P〗_n;K_1), (Pn ; S1) , (Pn ; S2 ) and (Pn,; S3 ) are arithmetic graphs.