Related papers: A classification of Mengerian $4$-uniform hypergra…
Given a set D of nonnegative integers, we derive the asymptotic number of graphs with a givenvnumber of vertices, edges, and such that the degree of every vertex is in D. This generalizes existing results, such as the enumeration of graphs…
We give a complete characterization of mixed unit interval graphs, the intersection graphs of closed, open, and half-open unit intervals of the real line. This is a proper superclass of the well known unit interval graphs. Our result solves…
All quasi-affine connected Generalized Dynkin Diagram with rank $= 4$ are found. All quasi-affine Nichols (Lie braided) algebras with rank $ 4$ are also found.
We find a set of generators for the automorphism group of a graph product of finitely generated abelian groups entirely from a certain labeled graph. In addition, we find generators for the important subgroup of star-automorphisms defined…
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.
We give a recursion formula to generate all equivalence classes of biconnected graphs with coefficients given by the inverses of the orders of their groups of automorphisms. We give a linear map to produce a connected graph with say, u,…
This article investigates the isomorphism problem for graphs derived from the four standard graph products: Cartesian, Kronecker (direct), strong, and lexicographic product. We provide a complete characterization of all simple connected…
We describe computational results about undirected graphs having $10$ vertices and automorphism group isomorphic to $\mathbb{Z}/4\mathbb{Z}$.
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…
We give the classification of all possible G-graphs for any small binary dihedral subgroup G in GL(2,C) and use this classification to give the combinatorial description of the special representations of G in terms of its maximal cyclic…
A categorical formalism for directed graphs is introduced, featuring natural notions of morphisms and subgraphs, and leading to two elementary descriptions of the free-properad monad, first in terms of presheaves on elementary graphs,…
Let $X$ be a family of graphs and $X_n$ the set of $n$-vertex graphs in $X$. A graph $U^{(n)}$ containing all graphs from $X_n$ as induced subgraphs is called $n$-universal for $X$. Moreover, we say that $U^{(n)}$ is a proper $n$-universal…
k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop the theory of covering spaces for k-graphs, obtaining a…
Hypergraphs are an invaluable tool to understand many hidden patterns in large data sets. Among many ways to represent hypergraph, one useful representation is that of weighted clique expansion. In this paper, we consider this…
A method for identifying graphs using MD5 hashing is presented. This allows fast graph equality comparisons and can also be used to facilitate graph isomorphism testing. The graphs can be labeled or unlabeled. The method identifies vertices…
We prove that for every integer $r\geq 2$, an $n$-vertex $k$-uniform hypergraph $H$ containing no $r$-regular subgraphs has at most $(1+o(1)){{n-1}\choose{k-1}}$ edges if $k\geq r+1$ and $n$ is sufficiently large. Moreover, if…
The $(n,k)$-star graphs are an important class of interconnection networks that generalize star graphs, which are superior to hypercubes. In this paper, we continue the work begun by Cheng et al.~(Graphs and Combinatorics 2017) and complete…
The class of intersection bigraphs of unit intervals of the real line whose ends may be open or closed is called a class of mixed unit interval bigraphs. This class of bigraphs is a strict superclass of the class of unit interval bigraphs.…
The notions of spectral measures and spectral classes, which are well known for graphs, are generalized and investigated for oriented hypergraphs.
A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper, $4$-valent one-regular graphs of order $5p^2$, where $p$ is a prime, are classified