zbMATH — the first resource for mathematics

A note on the McKay-Miller-Širáň graphs. (English) Zbl 1024.05039
Summary: B. D. McKay, M. Miller and J. Širáň [J. Comb. Theory, Ser. B 74, 110-118 (1998; Zbl 0911.05031)] constructed a family of the currently largest known vertex-transitive graphs of degree \(d\), diameter 2, and order \({8\over 9}(d+{1\over 2})^2\), for infinitely many values of \(d\). We present a simplified construction of their graphs.

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
Full Text: DOI
[1] Branković, L.; Miller, M.; Plesnı́k, J.; Ryan, J.; Širáň, J., Large graphs with small diameter and degree: A voltage assignment approach, Australasian J. combin., 18, 65-76, (1998) · Zbl 0929.05040
[2] Branković, L.; Miller, M.; Plesnı́k, J.; Ryan, J.; Širáň, J., A note on constructing large Cayley graphs of given degree and diameter by voltage assignments, Electron. J. combin., 5, R9, (1998) · Zbl 0885.05071
[3] Dineen, M.J.; Hafner, P.R., New results for the degree/diameter problem, Networks, 24, 359-367, (1994) · Zbl 0806.05039
[4] Erdős, P.; Fajtlowicz, S.; Hoffman, A.J., Maximum degree in graphs of diameter 2, Networks, 10, 87-90, (1980) · Zbl 0427.05042
[5] Hafner, P.R., Large Cayley graphs and digraphs with small degree and diameter, (), 291-302 · Zbl 0830.05025
[6] Gross, J.L.; Tucker, T.W., Topological graph theory, (1987), Wiley New York · Zbl 0621.05013
[7] McKay, B.D.; Miller, M.; Širáň, J., A note on large graphs of diameter two and given maximum degree, J. combin. theory ser. B, 74, 110-118, (1998) · Zbl 0911.05031
[8] Šiagiová, J., Composition of regular coverings of graphs, J. electrical engg., 50, 75-77, (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.