Geodesic
The classification of \(2\)-extendable edge-regular graphs with diameter \(2\)
Klavdija Kutnar1 ; Dragan Marušič1 ; Štefko Miklavič1 ; Primož Šparl2
1University of Primorska
2University of Ljubljana, University of Primorska
The electronic journal of combinatorics, Tome 26 (2019) no. 1
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Let $\ell$ denote a non-negative integer. A connected graph $\Gamma$ of even order at least $2\ell+2$ is $\ell$-extendable if it contains a matching of size $\ell$ and if every such matching is contained in a perfect matching of $\Gamma$. A connected regular graph $\Gamma$ is edge-regular, if there exists an integer $\lambda$ such that every pair of adjacent vertices of $\Gamma$ have exactly $\lambda$ common neighbours. In this paper we classify $2$-extendable edge-regular graphs of even order and diameter $2$.
DOI : 10.37236/8073
Classification : 05C70, 05C12

Klavdija Kutnar  1   ; Dragan Marušič  1   ; Štefko Miklavič  1   ; Primož Šparl  2

1 University of Primorska
2 University of Ljubljana, University of Primorska 
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     author = {Klavdija Kutnar and Dragan Maru\v{s}i\v{c} and \v{S}tefko Miklavi\v{c} and Primo\v{z} \v{S}parl},
     title = {The classification of \(2\)-extendable edge-regular graphs with diameter \(2\)},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {1},
     doi = {10.37236/8073},
     zbl = {1409.05160},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8073/}
}
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Klavdija Kutnar; Dragan Marušič; Štefko Miklavič; Primož Šparl. The classification of \(2\)-extendable edge-regular graphs with diameter \(2\). The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/8073

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