Large vertex-transitive graphs of diameter 2 from incidence graphs of biaffine planes

Balbuena, C.; Miller, Mirka; Širáň‬, Jozef; Ždímalová, Mária

doi:10.1016/j.disc.2013.03.007

Cited by 6 publications

(5 citation statements)

References 8 publications

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“…The graph C q is also known as the incidence graph of the biaffine plane [18] and it has been used to find extremal graphs without short cycles (see [1][2][3][4][5][6][7][8][9][10]21]). The graph C q is q-regular of order 2q 2 , has girth g = 6 for q ≥ 3 and it is vertex transitive.…”

Section: Amalgamating Into Elliptic Semiplanes Of Type Cmentioning

confidence: 99%

New small regular graphs of girth 5

Abajo

Araujo‐Pardo²,

Balbuena

et al. 2017

Discrete Mathematics

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Section: Amalgamating Into Elliptic Semiplanes Of Type Cmentioning

confidence: 99%

New small regular graphs of girth 5

Abajo

Araujo‐Pardo²,

Balbuena

et al. 2017

Discrete Mathematics

Self Cite

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“…Moreover, the graphs constructed by these authors are vertex transitive, in particular the graph G q, q−1 4 for any q ≡ 1 (mod 4) odd prime power is vertex transitive. Furthermore, in [2] there is a complete discussion devoted to symmetries and automorphism groups of these graphs and other related issues.…”

Section: Basic Constructionmentioning

confidence: 99%

A family of mixed graphs with large order and diameter 2

Araujo‐Pardo

Balbuena

Miller³

et al. 2017

Discrete Applied Mathematics

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A mixed regular graph is a connected simple graph in which each vertex has both a fixed outdegree (the same indegree) and a fixed undirected degree. A mixed regular graphs is said to be optimal if there is not a mixed regular graph with the same parameters and bigger order.\ud We present a construction that provides mixed graphs of undirected degree qq, directed degree View the MathML sourceq-12 and order 2q22q2, for qq being an odd prime power. Since the Moore bound for a mixed graph with these parameters is equal to View the MathML source9q2-4q+34 the defect of these mixed graphs is View the MathML source(q-22)2-14.\ud In particular we obtain a known mixed Moore graph of order 1818, undirected degree 33 and directed degree 11 called Bosák’s graph and a new mixed graph of order 5050, undirected degree 55 and directed degree 22, which is proved to be optimal.Peer ReviewedPostprint (author's final draft

show abstract

“…Moreover, the graphs constructed by these authors are vertex transitive, in particular the graph G q, q−1 4 for any q ≡ 1(mod 4) odd prime power is vertex transitive. Furthermore, in [2] there is a complete discussion devoted to symmetries and automorphism groups of these graph and other related issues.…”

Section: Basic Constructionmentioning

confidence: 99%