Recursive constructions of small regular graphs of given degree and girth

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• 作者：Geoffrey Exoo ; Robert Jajcay
• 关键词：Cage ; Recursive construction ; Geometric graph ; Paley graph ; Cayley map
• 刊名：Discrete Mathematics
• 出版年：2012
• 出版时间：6 September, 2012
• 年：2012
• 卷：312
• 期：17
• 页码：2612-2619
• 全文大小：294 K

文摘

We revisit and generalize a recursive construction due to Sachs involving two graphs which increases the girth of one graph and the degree of the other. We investigate the properties of the resulting graphs in the context of cages and construct families of small graphs using geometric graphs, Paley graphs, and techniques from the theory of Cayley maps.