Elsevier

Discrete Mathematics

Volume 4, Issue 2, February 1973, Pages 129-138
Discrete Mathematics

Further characterizations of cubic lattice graphs

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Abstract

A cubic lattice graph with characteristic n is a graph whose points can be identified with the ordered triplets on n symbols and two points are adjacent whenever the corresponding triplets have two coordinates in common. An L2 graph is a graph whose points can be identified with the ordered pairs on n symbols such that two points are adjacent if and only if the corresponding pairs have a common coordinate. The main result of this paper is two new characterizations and shows the relation between cubic lattice and L2 graphs. The main result also suggests a conjecture concerning the characterization of interchange graphs of complete m-partite graphs.

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