Results 31 to 40 of about 452 (178)

Cayley graphs of basic algebraic structures [PDF]

Discrete Mathematics & Theoretical Computer Science, 2020
We present simple graph-theoretic characterizations for the Cayley graphs of monoids, right-cancellative monoids, left-cancellative monoids, and groups.
Didier Caucal
doaj   +1 more source

Integral Cayley Sum Graphs and Groups

Discussiones Mathematicae Graph Theory, 2016
For any positive integer k, let Ak denote the set of finite abelian groups G such that for any subgroup H of G all Cayley sum graphs CayS(H, S) are integral if |S| = k. A finite abelian group G is called Cayley sum integral if for any subgroup H of G all
Ma Xuanlong, Wang Kaishun
doaj   +1 more source

Quartic integral Cayley graphs

Ars Mathematica Contemporanea, 2015
We give exhaustive lists of connected 4-regular integral Cayley graphs and connected 4-regular integral arc-transitive graphs. An integral graph is a graph for which all eigenvalues are integers. A Cayley graph Cay(Γ, S) for a given group Γ and connection set S ⊂ Γ is the graph with vertex set Γ and with a connected to b if and only if ba−1 ∈ S.
Minchenko, Marsha, Wanless, Ian M.
openaire   +3 more sources

COMPUTING THE EIGENVALUES OF CAYLEY GRAPHS OF ORDER p2q [PDF]

Journal of Algebraic Systems, 2020
A graph is called symmetric if its full automorphism group acts transitively on the set of arcs. The Cayley graph $Gamma=Cay(G,S)$ on group $G$ is said to be normal symmetric if $N_A(R(G))=R(G)rtimes Aut(G,S)$ acts transitively on the set of arcs of ...
M. Ghorbani, A. Seyyed-Hadi, F. Nowroozi-Larki   +2 more
doaj   +1 more source

Uniquely colorable Cayley graphs

Ars Mathematica Contemporanea, 2016
It is shown that the chromatic number χ ( G ) =  k of a uniquely colorable Cayley graph G over a group Γ  is a divisor of ∣Γ ∣ =  n . Each color class in a k -coloring of G is a coset of a subgroup of order n  /  k of Γ  . Moreover, it is proved that ( k  − 1) n is a sharp lower bound for the number of edges of a uniquely k
Klotz, Walter, Sander, Torsten
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Domination Parameters of the Unitary Cayley Graph of 𝕑/n𝕑

Discussiones Mathematicae Graph Theory, 2023
The unitary Cayley graph of 𝕑/n𝕑, denoted Xn, is the graph with vertex set {0, . . ., n − 1} where vertices a and b are adjacent if and only if gcd(a − b, n) = 1.
Burcroff Amanda
doaj   +1 more source

On the metric dimension of Cayley graphs

AKCE International Journal of Graphs and Combinatorics, 2022
In this paper, we investigate the metric dimension, local metric dimension and edge metric dimension for some (generalized) Cayley graphs.
Afsaneh Rezaei, Kazem Khashyarmanesh, Mojgan Afkhami   +2 more
doaj   +1 more source

Mixed Moore Cayley Graphs [PDF]

Journal of Interconnection Networks, 2017
The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. There has been much recent interest in the problem for mixed graphs, where we allow both undirected edges and directed arcs in the graph.
openaire   +2 more sources

A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A₁₁₉

Mathematics, 2021
A Cayley graph Γ=Cay(G,S) is said to be normal if the base group G is normal in AutΓ. The concept of the normality of Cayley graphs was first proposed by M.Y.
Bo Ling, Wanting Li, Bengong Lou
doaj   +1 more source

Dimer models and conformal structures

Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 340-446, February 2026.
Abstract Dimer models have been the focus of intense research efforts over the last years. Our paper grew out of an effort to develop new methods to study minimizers or the asymptotic height functions of general dimer models and the geometry of their frozen boundaries.
Kari Astala, Erik Duse, István Prause, Xiao Zhong   +3 more
wiley   +1 more source