Geodesic
Edge regular graph products
Boštjan Frelih1 ; Štefko Miklavič1
1University of Primorska
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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A regular nonempty graph $\Gamma$ is called edge regular, whenever there exists a nonegative integer $\lambda_{\Gamma}$, such that any two adjacent vertices of $\Gamma$ have precisely $\lambda_{\Gamma}$ common neighbours. An edge regular graph $\Gamma$ with at least one pair of vertices at distance 2 is called amply regular, whenever there exists a nonegative integer $\mu_{\Gamma}$, such that any two vertices at distance 2 have precisely $\mu_{\Gamma}$ common neighbours. In this paper we classify edge regular graphs, which can be obtained as a strong product, or a lexicographic product, or a deleted lexicographic product, or a co-normal product of two graphs. As a corollary we determine which of these graphs are amply regular.
DOI : 10.37236/2817
Classification : 05C75, 05C76
Mots-clés : edge regular graph, graph products, amply regular graphs

Boštjan Frelih  1   ; Štefko Miklavič  1

1 University of Primorska 
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     title = {Edge regular graph products},
     journal = {The electronic journal of combinatorics},
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Boštjan Frelih; Štefko Miklavič. Edge regular graph products. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2817

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