Seminár z algebratickej teórie grafov - Ajda Zavrtanik Drglin (14.12.2018)

v piatok 14.12.2018 o 13:30 hod. v miestnosti M/XI

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Prednášajúci: Ajda Zavrtanik Drglin 

Názov: Some results on edge-girth-regular graphs

Termín: 14.12.2018, 13:30 hod., M/XI

Abstrakt:
We say that a $k$-regular graph $\Gamma$ with $|V(\Gamma)|=v$ and girth $g$ is \emph{edge-girth-regular} with parameters $(v, k, g, \lambda)$ if every edge of $\Gamma$ lies on exactly $\lambda$ cycles of length $g$. We denote such a graph as an $egr(v, k, g, \lambda)$ graph. We explore some properties of edge-girth-regular graphs, find the smallest $v$ such that an $egr(v, 4, 3, 1) $ graph exist and prove the graph is unique. We try to find the smallest $v$ such that an $egr(v, 4, 4, 1)$ graph exist and look at the restriction of this problem to bipartite graphs, which we generalise for all $k$ and $g$. We then take a look at Cayley graphs and analyse the possible spectrum for $\lambda$ for $egr(v, 4, 4, \lambda)$ Cayley graphs of abelian groups.

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