A characterization of Tutte-Coxeter graph
Mohammad Farrokhi Derakhshandeh Ghouchan, Abbas Mohammadian
TL;DR
This paper introduces a generalized family of Tutte-Coxeter graphs and proves the uniqueness of the original graph as the only vertex- and edge-transitive member within this family.
Contribution
It provides a natural generalization of the Tutte-Coxeter graph and establishes its uniqueness among generalized graphs with vertex- and edge-transitivity.
Findings
Tutte-Coxeter graph is unique among generalized graphs with vertex- and edge-transitivity.
A natural generalization of the Tutte-Coxeter graph is constructed.
The original Tutte-Coxeter graph is characterized by its symmetry properties.
Abstract
We give a natural generalization of the Tutte-Coxeter graph in a natural way and prove that the Tutte-Coxeter graph is the only vertex-transitive (edge-transitive) graph among all generalized Tutte-Coxeter graphs.
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · semigroups and automata theory