相关论文: Properties of Full-Flag Johnson Graphs
Assume that there is a free group action of automorphisms on a bipartite graph. If there is a perfect matching on the factor graph, then obviously there is a perfect matching on the graph. Surprisingly, the reversed is also true for…
Let $S$ be a non-empty finite set. A flag of $S$ is a set $f$ of non-empty proper subsets of $S$ such that $X\subseteq Y$ or $Y\subseteq X$ for all $X,Y\in f$. The set $\{|X|:X\in f\}$ is called the type of $f$. Two flags $f$ and $f'$ are…
We consider the family of undirected Cayley graphs associated with odd cyclic groups, and study statistics for the eigenvalues in their spectra. Our results are motivated by analogies between arithmetic geometry and graph theory.
A number of authors have studied the question of when a graph can be represented as a Cayley graph on more than one nonisomorphic group. In this paper we give conditions for when a Cayley graph on an abelian group can be represented as a…
Let $G$ be a finite, undirected $d$-regular graph and $A(G)$ its normalized adjacency matrix, with eigenvalues $1 = \lambda_1(A)\geq \dots \ge \lambda_n \ge -1$. It is a classical fact that $\lambda_n = -1$ if and only if $G$ is bipartite.…
We study the class of 1-perfectly orientable graphs, that is, graphs having an orientation in which every out-neighborhood induces a tournament. 1-perfectly orientable graphs form a common generalization of chordal graphs and circular arc…
The $\alpha$-Hermitian adjacency matrix $H_\alpha$ of a mixed graph $X$ has been recently introduced. It is a generalization of the adjacency matrix of unoriented graphs. In this paper, we consider a special case of the complex number…
A graph is said to be uniquely hamiltonian if it has a unique hamiltonian cycle. For a natural extension of this concept to infinite graphs, we find all uniquely hamiltonian vertex-transitive graphs with finitely many ends, and also discuss…
Graph polynomials are deemed useful if they give rise to algebraic characterizations of various graph properties, and their evaluations encode many other graph invariants. Algebraic: The complete graphs $K_n$ and the complete bipartite…
Due to their elegant and simple nature, unitary Cayley graphs have been an active research topic in the literature. These graphs are naturally connected to several branches of mathematics, including number theory, finite algebra,…
A new complete invariant for acyclic graphs is presented
We consider Cayley sum graphs over the cyclic group $\mathbb{Z}_n$ and aim to explore several necessary and sufficient conditions for the existence of total perfect codes in these graphs. Specifically, we examine various cases for the…
We introduce jacobian graphs, which are explicit families of regular graphs that are spectrally indistinguishable from random graphs, but whose local structure is very different from that of random graphs. The construction relies on the…
In present article, we determine the distinguishing number of the merged Johnson graphs which are generalization of both the Kneser graphs and of the Johnson graphs.
Motivated by an approach to visualization of high dimensional statistical data given in Hurley and Oldford (2011), this work examines the clique structure of $J_n(m, m-1)$ Johnson graphs. Cliques and maximal cliques are characterized and…
We show that the star graph defined as the Cayley graph of ${\mathfrak S}_{n+1}$ generated by the star transpositions is an ${\mathfrak S}_n$-cover of the complete graph $K_{n+1}$, which is known to have fine spectral properties. In the…
We investigate prime character degree graphs of solvable groups. In particular, we consider a family of graphs $\Gamma_{k,t}$ constructed by adjoining edges between two complete graphs in a one-to-one fashion. In this paper we determine…
When dealing with symmetry properties of mathematical objects, one of the fundamental questions is to determine their full automorphism group. In this paper this question is considered in the context of even/odd permutations dichotomy. More…
A connected symmetric graph of prime valency is {\em basic} if its automorphism group contains no nontrivial normal subgroup having more than two orbits. Let $p$ be a prime and $n$ a positive integer. In this paper, we investigate…
We focus on two specific generalizations of the chromatic symmetric function: one involving universal graphs and the other concerning vertex-weighted graphs. In this paper, we introduce a unified generalization that incorporates both…