• On Distance Divisor Symmetric n-Sigraphs

Abstract

An n-tuple (a_1,a_2,…,a_n) is symmetric, if a_k=a_(n-k+1),1≤k≤n. Let H_n={(a_1,a_2,…,a_n ): a_k∈{+,-}, a_k=a_(n-k+1), 1≤k≤n} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair Sn = (G, σ) (Sn = (G, µ)), where G = (V, E) is a graph called the underlying graph of Sn and σ: E → Hn (µ: V → Hn) is a function. In this paper, we introduced a new notion distance divisor symmetric n-sigraph of a symmetric n-sigraph and its properties are obtained. Also, we obtained the structural characterization of distance divisor symmetric n-signed graphs.