Jana Šiagiová

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Steven J. Miller

Williams College

Marc Champagne

Kwantlen Polytechnic University

Cheryl Praeger

The University of Western Australia

Cenap Ozel

King Abdulaziz University

Ibrahim Cahit

Near East University

Umberto Cerruti

Università degli Studi di Torino

Nasreen Kausar

Yildiz Technical University

Tomasz Szemberg

University of the National Education Commission in Krakow

Jack Graver

Syracuse University

Oliver Knill

Harvard University

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Papers by Jana Šiagiová

Asymptotically approaching the Moore bound for diameter three by Cayley graphs

Journal of Combinatorial Theory, Series B

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Asymptotically approaching the Moore bound for diameter three by Cayley graphs

Journal of Combinatorial Theory, Series B

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Large vertex-transitive and Cayley graphs with given degree and diameter

We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that... more We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that arise as lifts of dipoles with voltage assignments in Abelian groups. Further, we construct a family of Cayley graphs of degree d =3 m − 1 and diameter k ≥ 3 of order kmk. By comparison with other available results in this area we show that, for sufficiently large d and k such that k ≤ d − 2, our family gives the current largest known Cayley graphs of degree d and diameter k.

A note on large Cayley graphs of diameter two and given degree

For a variety of infinite sets of positive integers d related to odd prime powers we describe a s... more

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Small vertex-transitive and Cayley graphs of girth six and given degree: an algebraic approach

by Jana Šiagiová and Mirka Miller

We examine the existing constructions of the smallest known vertex-transitive graphs of a given d... more We examine the existing constructions of the smallest known vertex-transitive graphs of a given degree and girth 6. It turns out that most of these graphs can be described in terms of regular lifts of suitable quotient graphs. A further outcome of our analysis is a precise identification of which of these graphs are Cayley. We also investigate higher level of transitivity of the smallest known vertex-transitive graphs of a given degree and girth 6 and relate their constructions to near-difference sets. ᭧

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Large Cayley graphs and vertex-transitive non-Cayley graphs of given degree and diameter

For any d ≥ 5 and k ≥ 3 we construct a family of Cayley graphs of degree d, diameter k, and order... more

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Small vertex-transitive and Cayley graphs of girth six and given degree: an algebraic approach

Journal of Graph Theory, 2011

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Approaching the Moore bound for diameter two by Cayley graphs

Journal of Combinatorial Theory, Series B, 2012

The order of a graph of maximum degree d and diameter 2 cannot exceed d 2 + 1, the Moore bound fo... more The order of a graph of maximum degree d and diameter 2 cannot exceed d 2 + 1, the Moore bound for diameter two. A combination of known results guarantees the existence of regular graphs of degree d, diameter 2, and order at least d 2 − 2d 1.525 for all sufficiently large d, asymptotically approaching the Moore bound. The corresponding graphs, however, tend to have a fairly small or trivial automorphism group and the nature of their construction does not appear to allow for modifications that would result in a higher level of symmetry. The best currently available construction of vertex-transitive graphs of diameter 2 and preassigned degree gives order 8 9 (d + 1 2 ) 2 for all degrees of the form d = (3q − 1)/2 for prime powers q ≡ 1 mod 4.

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