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Smallest Vertex‐Transitive Graphs of Given Degree and Diameter
Authors:Martin Knor  Jozef ?iráň
Institution:1. DEPARTMENT OF MATHEMATICS, FACULTY OF CIVIL ENGINEERING, SLOVAK UNIVERSITY OF TECHNOLOGY IN BRATISLAVA, RADLINSKéHO 11, SLOVAKIA;2. DEPARTMENT OF MATHEMATICS AND STATISTICS, THE OPEN UNIVERSITY, MILTON KEYNES, UNITED KINGDOM
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.
Keywords:extremal problem  degree/diameter problem  vertex‐transitive graph  Cayley graph  smallest graph
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