In this paper, we give a survey of spanning trees. We mainly deal with spanning trees having
some particular properties concerning a hamiltonian properties, for example, spanning trees …

To observe and control a networked system, especially in failure-prone circumstances, it is
imperative that the underlying network structure be robust against node or link failures. A …

Connectivity is one of the most basic concepts of graph-theoretical subjects, both in a
combinatorial sense and in an algorithmic sense. As we know, the classical connectivity has …

Abstract Graph Factors and Matching Extensions deals with two important branches of graph
theory-factor theory and extendable graphs. Due to the mature techniques and wide ranges …

The purpose of this article is to introduce several results concerning the analysis and
synthesis of reliable or invulnerable networks. First, the notion of signed reliability …

Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and
eigenvectors of matrices associated with graphs to study them. In this paper, we present a …

We relate homological properties of a binomial edge ideal $\mathcal {J} _G $ to invariants
that measure the connectivity of a simple graph $ G $. Specifically, we show if $ R/\mathcal …

The study of the existence of Hamiltonian cycles in a graph is a classical problem in graph
theory. By incorporating toughness and spectral conditions, we can consider Chvátal's …

The toughness t (G) of a graph G=(V, E) is defined as t (G)= min {| S| c (G− S)}, in which the
minimum is taken over all S⊂ V such that G− S is disconnected, where c (G− S) denotes the …

The eigenvalues of graphs are related to many of its combinatorial properties. In his
fundamental work, Fiedler showed the close connections between the Laplacian …