An Algorithm for the Influential Hinge Vertex Problem on Interval Graphs

抄録

Consider a simple undirected graph G = (V, E) with vertex set V and edge set E. The distance δ_G(x, y) is defined as the length of the shortest path between vertices x and y in G. The vertex u ∈ V is a hinge vertex if there exist two vertices x, y ∈ V - {u} such that δ_{G - u}(x, y) > δ_G(x, y). Let U be a set consisting of all hinge vertices of G, and let AVS(u) denote the set of pairs of vertices (x, y)s to which a path between x and y becomes longer after removal of a hinge vertex u from G. The influential hinge vertex problem aims to determine the hinge vertex u that maximizes |AVS(u)| in G. In this study, we propose an algorithm that runs in O(n²) time to solve the influential hinge vertex problem on an interval graph.