Graphs of order two less than the Moore bound |
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| Authors: | Mirka Miller |
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| Institution: | a School of Information Technology and Mathematical Sciences, University of Ballarat, Vic 3353, Australia
b Combinatorial Mathematics Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia |
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| Abstract: | The problem of determining the largest order nd,k of a graph of maximum degree at most d and diameter at most k is well known as the degree/diameter problem. It is known that nd,k?Md,k where Md,k is the Moore bound. For d=4, the current best upper bound for n4,k is M4,k-1. In this paper we study properties of graphs of order Md,k-2 and we give a new upper bound for n4,k for k?3. |
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| Keywords: | Moore bound Degree/diameter problem Undirected graphs |
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