Homomorphisms of Strongly Regular Graphs

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• 作者：David E. Roberson¹ ; ^{davideroberson@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：graph homomorphisms ; strongly regular graphs ; Lová ; sz theta ; cores
• 刊名：Electronic Notes in Discrete Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：54
• 期：Complete
• 页码：271-276
• 全文大小：180 K

文摘

We prove that if G and H are primitive strongly regular graphs with the same parameters and ϕ is a homomorphism from G to H, then ϕ is either an isomorphism or a coloring (homomorphism to a complete subgraph). Moreover, any such coloring is optimal for G and its image is a maximum clique of H. Therefore, the only endomorphisms of a primitive strongly regular graph are automorphisms or colorings. This confirms and strengthens a conjecture of Peter Cameron and Priscila Kazanidis that all strongly regular graphs are cores or have complete cores. The proof of the result is elementary, mainly relying on linear algebraic techniques.