Related papers: Cordial Deficiency
The family of Directed Acyclic Graphs as well as some related graphs are analyzed with respect to extremal behavior in relation with the family of intersection graphs for families of boxes with transverse intersection.
An almost self-centered graph is a connected graph of order $n$ with exactly $n-2$ central vertices, and an almost peripheral graph is a connected graph of order $n$ with exactly $n-1$ peripheral vertices. We determine (1) the maximum girth…
Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…
We study here the graphs with seven vertices in an effort to classify which of them appear as the prime character degree graphs of finite solvable groups. This classification is complete for the disconnected graphs. Of the 853…
An $n$-vertex graph whose degree set consists of exactly $n-1$ elements is called antiregular graph. Such type of graphs are usually considered opposite to the regular graphs. An irregularity measure ($IM$) of a connected graph $G$ is a…
The purpose of this paper is to develop a "calculus" on graphs that allows graph theory to have new connections to analysis. For example, our framework gives rise to many new partial differential equations on graphs, most notably a new…
This paper considers the degree-diameter problem for undirected circulant graphs. For degrees 10 and 11 newly discovered families of circulant graphs of arbitrary diameter are presented which are largest known and are conjectured to be…
Binary classification problems can be naturally modeled as bipartite graphs, where we attempt to classify right nodes based on their left adjacencies. We consider the case of labeled bipartite graphs in which some labels and edges are not…
We show that the abelian girth of a graph is at least three times its girth. We prove an analogue of the Moore bound for the abelian girth of regular graphs, where the degree of the graph is fixed and the number of vertices is large. We…
We prove distance bounds for graphs possessing positive Bakry-\'Emery curvature apart from an exceptional set, where the curvature is allowed to be non-positive. If the set of non-positively curved vertices is finite, then the graph admits…
We investigate structural and combinatorial properties of Bi-Cayley graphs defined over cyclic groups of order $p^2q^2$, where $p$ and $q$ are distinct primes. We begin by describing their fundamental group-theoretic underpinnings. The main…
In this paper, we propose two novel approaches for hypergraph comparison. The first approach transforms the hypergraph into a graph representation for use of standard graph dissimilarity measures. The second approach exploits the…
The study of networks characteristics is an important subject in different fields, like math, chemistry, transportation, social network analysis etc. The residual closeness is one of the most sensitive measure of graphs vulnerability. In…
In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph into a new graph which is called the Mycielskian of that graph. In this paper we provide some…
Using the two way distance, we introduce the concepts of weak metric dimension of a strongly connected digraph $\Gamma$. We first establish lower and upper bounds for the number of arcs in $\Gamma$ by using the diameter and weak metric…
To lowest-order weak interactions in the standard model, we point out that a complete graph description of two-body mesonic $B$ (or $D$) decays needs ten topologically different quark diagrams. The two-body baryonic $B$ decays can be…
Mixed graphs can be seen as digraphs with arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which the undirected and directed degrees are one. The best graphs,…
We introduce a new family of graphs, namely, hybrid graphs. There are infinitely many hybrid graphs associated to a single graph. We show that every hybrid graph associated to a given graph is Cohen Macaulay. Furthermore, we show that every…
We determine a lower bound for the number of edges of a 2-connected maximal nontraceable graph, and present a construction of an infinite family of maximal nontraceable graphs that realize this bound.
Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social…