On orbital regular graphs and Frobenius graphs

X.G. Fang; Cai-Heng Li; Cheryl Praeger

doi:10.1016/S0012-365X(97)00148-9

On orbital regular graphs and Frobenius graphs

X.G. Fang, Cai-Heng Li, Cheryl Praeger

Graduate Research School

Research output: Contribution to journal › Article

15 Citations (Scopus)

Abstract

A graph is called a Frobenius graph if it is a connected orbital graph of a Frobenius group. In this paper, we show first that almost all orbital regular graphs are Frobenius graphs. Then we give a description of Frobenius graphs in terms of a family of (usually smaller) Frobenius graphs which are Cayley graphs for elementary abelian groups. Finally, based on this description, we obtain a formula for calculating the edge-forwarding index of Frobenius graphs.

Original language	English
Pages (from-to)	85-99
Journal	Discrete Mathematics
Volume	182
DOIs	https://doi.org/10.1016/S0012-365X(97)00148-9
Publication status	Published - 1998

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Fang, X. G., Li, C-H., & Praeger, C. (1998). On orbital regular graphs and Frobenius graphs. Discrete Mathematics, 182, 85-99. https://doi.org/10.1016/S0012-365X(97)00148-9

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N2 - A graph is called a Frobenius graph if it is a connected orbital graph of a Frobenius group. In this paper, we show first that almost all orbital regular graphs are Frobenius graphs. Then we give a description of Frobenius graphs in terms of a family of (usually smaller) Frobenius graphs which are Cayley graphs for elementary abelian groups. Finally, based on this description, we obtain a formula for calculating the edge-forwarding index of Frobenius graphs.

AB - A graph is called a Frobenius graph if it is a connected orbital graph of a Frobenius group. In this paper, we show first that almost all orbital regular graphs are Frobenius graphs. Then we give a description of Frobenius graphs in terms of a family of (usually smaller) Frobenius graphs which are Cayley graphs for elementary abelian groups. Finally, based on this description, we obtain a formula for calculating the edge-forwarding index of Frobenius graphs.

U2 - 10.1016/S0012-365X(97)00148-9

DO - 10.1016/S0012-365X(97)00148-9

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JF - Discrete Mathematics

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Access to Document

10.1016/S0012-365X(97)00148-9