Related papers: On the relation between connectivity, independence…
This paper studies coordination problem for time-varying networks suffering from antagonistic information, quantified by scaling parameters. By such a manner, interacting property of the participating individuals and antagonistic…
We show that for every graph $G$ that contains two edge-disjoint spanning trees, we can choose two edge-disjoint spanning trees $T_1,T_2$ of $G$ such that $|d_{T_1}(v)-d_{T_2}(v)|\leq 5$ for all $v \in V(G)$. We also prove the more general…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
The primary objective of this paper is to investigate the notions of geometric and sequential convexity within a graph-theoretic framework, with the aim of examining various structural properties and exploring the connection between these…
Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us…
The distance matrix of a connected graph is the symmetric matrix with columns and rows indexed by the vertices and entries that are the pairwise distances between the corresponding vertices. We give a construction for graphs which differ in…
An independent set in a graph is a set of pairwise non-adjacent vertices. The independence number $\alpha{(G)}$ is the size of a maximum independent set in the graph $G$. The independence polynomial of a graph is the generating function for…
The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear…
We continue the study of $(tw,\omega)$-bounded graph classes, that is, hereditary graph classes in which large treewidth is witnessed by the presence of a large clique, and the relation of this property to boundedness of the…
This paper is a short introduction to the theory of tangles, both in graphs and general connectivity systems. An emphasis is put on the correspondence between tangles of order k and k-connected components. In particular, we prove that there…
The independence polynomial of a hypergraph is the generating function for its independent (vertex) sets with respect to their cardinality. This article aims to discuss several recurrence relations for the independence polynomial using some…
Let $D$ be a connected weighted digraph. The relation between the vertex weighted complexity (with a fixed root) of the line digraph of $D$ and the edge weighted complexity (with a fixed root) of $D$ has been given in (L. Levine, Sandpile…
Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely applicable and extensively studied combinatorial objects. We initiate the study of such highly connected graphs that are, in…
Since Darwin, species trees have been used as a simplified description of the relationships which summarize the complicated network $N$ of reality. Recent evidence of hybridization and lateral gene transfer, however, suggest that there are…
Determining and analyzing the spectra of graphs is an important and exciting research topic in theoretical computer science. The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on…
An independent set in a simple graph $G$ is a set of pairwise non-adjacent vertices in $G$. The independence polynomial of $G$, denoted by $I_G$ is defined as $1 + a_1 z + a_2 z^2+\cdots+a_d z^{d}$, where $a_i$ denotes the number of…
We generalize two main theorems of matching polynomials of undirected simple graphs, namely, real-rootedness and the Heilmann-Lieb root bound. Viewing the matching polynomial of a graph $G$ as the independence polynomial of the line graph…
In this paper we consider how the strong-coupling scale, or perturbative cutoff, in a multi-gravity theory depends upon the presence and structure of interactions between the different fields. This can elegantly be rephrased in terms of the…
We compute the total number of spanning trees for the generalized cone of the complete graph $K_n$ and a number of families of some modified bipartite graphs $K_{m,n}$. In particular, we obtain a new method of finding the number of spanning…
The independence complex of a graph G is a simplicial complex whose simplices are the independent sets in G. In the last couple of decades, the independence complexes of square grids (with various boundary conditions) have gained much…