Smallest Vertex-Transitive Graphs of Given Degree and Diameter

Authors

  • Martin Knor,

    1. DEPARTMENT OF MATHEMATICS, FACULTY OF CIVIL ENGINEERING, SLOVAK UNIVERSITY OF TECHNOLOGY IN BRATISLAVA, RADLINSKÉHO 11, SLOVAKIA
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  • Jozef Širáň

    1. DEPARTMENT OF MATHEMATICS AND STATISTICS, THE OPEN UNIVERSITY, MILTON KEYNES, UNITED KINGDOM
    2. DEPARTMENT OF MATHEMATICS, FACULTY OF CIVIL ENGINEERING, SLOVAK UNIVERSITY OF TECHNOLOGY IN BRATISLAVA, RADLINSKÉHO 11, SLOVAKIA
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  • Contract graph sponsor: VEGA; Contract grant number: 1/0781/11; Contract grant sponsor: APVV; Contract grant number: 0223-10; Contract grant sponsor: APVV-EUROCORES Programme EUROGIGA, project GREGAS; Contract grant number ESF-EC-0009-10.

Abstract

For every d and k, we determine the smallest order of a vertex-transitive graph of degree d and diameter k, and in each such case we show that this order is achieved by a Cayley graph.

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