A note on some distance-based topological indices of circulant network C_n(1, a)

Abstract

Let Г be a simple connected graph/network with vertex set V(Г) and edge set E(Г). A topological index is a real number associated to Г that characterizes its topology and is invariant under graph automorphism. If υ_i and υ_j are vertices in V(Г), the distance between them denoted by d_Г (υ_i, υ_j) refers to the length of the shortest path that connects υ_i, and υ_j. A topological index is said to be distance-based if its computation involves distance between vertices. Recently, the exact value of some distance-based topological indices namely Wiener, hyper-Wiener, and Schultz molecular topological index of the circulant network C_n(1, a) for a = 2, 3, 4, and 5 were computed. In this paper, we use the breadth-first search method to compute for some distance-based topological indices of the circulant network C_n(1, a) where a = 6 and . We also provide a general formula for the computation of the Wiener, Schultz, and Gutman index of the circulant network C_n(1, a) where .

Subject Classification:

• 05C09
• 05C12
• 05C85

Keywords:

• Circulant network
• Distance-based topological indices
• Distance spectral radius
• Vertex transmission