Affiliation:
1. School of Mathematical Sciences MOE‐LSC and SHL‐MAC Shanghai Jiao Tong University Shanghai China
Abstract
AbstractThe average distance of a simple connected graph is the average of the distances between all pairs of vertices in . We prove that for a connected cubic graph on vertices, , if ; and , if . Furthermore, all extremal graphs attaining the upper bounds are characterized, and they have the maximum possible diameter. The result solves a question of Plesník and proves a conjecture of Knor, Škrekovski, and Tepeh on the average distance of cubic graphs. The proofs use graph transformations and structural graph analysis.
Funder
Science and Technology Commission of Shanghai Municipality
National Natural Science Foundation of China
Subject
Geometry and Topology,Discrete Mathematics and Combinatorics