ON THE MAXIMAL DISTANCE SPECTRAL RADIUS IN A CLASS OF BICYCLIC GRAPHS

Abstract

Bicyclic graphs are connected graphs in which the number of edges equals the number of vertices plus one. Let Pp+1 = x1x2⋯xp+1, Pt+1 = y1y2⋯yt+1 and Pq+1 = z1z2⋯zq+1 be three vertex-disjoint paths. Identifying the initial vertices as u0 and the terminal vertices as v0, the resultant graph, denoted by θ(p; t; q), is called a θ-graph. Let [Formula: see text] be the class of all bicyclic graphs on n vertices, which contain a θ-graph as an induced subgraph. In this paper, we study the distance spectral radius of bicyclic graphs in [Formula: see text], and determine the graph with the largest distance spectral radius.