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.
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