Related papers: Maximum atom-bond connectivity index with given gr…
Quantifying the influence of microscopic details on the dynamics of development of the overall structure of a filamentous network is important in a number of biologically relevant contexts, but it is not obvious what order parameters can be…
For a graph $G$ without isolated vertices, the inverse degree of a graph $G$ is defined as $ID(G)=\sum_{u\in V(G)}d(u)^{-1}$ where $d(u)$ is the number of vertices adjacent to the vertex $u$ in $G$. By replacing $-1$ by any non-zero real…
This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set--Based Graph. The algorithm, under certain restrictions on those sets, has the…
The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph. It found considerable applications in a variety of fields. In this paper, we determine the minimum Kirchhoff…
We study the connectivity properties of random Bluetooth graphs that model certain "ad hoc" wireless networks. The graphs are obtained as "irrigation subgraphs" of the well-known random geometric graph model. There are two parameters that…
The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to…
We derive a new upper bound on the algebraic connectivity of a regular graph using the Higman-Sims technique. Together with a new result on the connectivity of the neighbourhood graph of strongly regular graphs, our result gives a…
Consider a graph whose vertices are colored in one of two colors, say black or white. A white vertex is called integrated if it has at least as many black neighbors as white neighbors, and similarly for a black vertex. The coloring as a…
Let $G$ be a connected graph with $n$ vertices and $m$ edges. The vertex-degree-based topological index (VDB) (or graphical function-index) $TI(G)$ of $G$ with edge-weight function $I(x,y)$ is defined as $$TI(G)=\sum\limits_{uv\in…
This work is devoted to establish a general expression for calculating the bond incident degree (BID) indices of polyomino chains and to characterize the extremal polyomino chains with respect to several well known BID indices. From the…
The connective eccentricity index $\xi^{ce}=\sum^{}_{u\in V}\frac{d(u)}{\varepsilon(u)}$, where $\varepsilon(u)$ and $d(u)$ denote the eccentricity and the degree of the vertex $u$, respectively. In this paper, we first determine the…
We determine the optimum topology of quasi-one dimensional nonlinear optical structures using generalized quantum graph models. Quantum graphs are relational graphs endowed with a metric and a multiparticle Hamiltonian acting on the edges,…
We present a new, novel approach to obtaining a network's connectivity. More specifically, we show that there exists a relationship between a network's graph isoperimetric properties and its conditional connectivity. A network's…
The association between tie strength and social structure is a fundamental topic in the social sciences. We study this association by analyzing tie strength in higher-order networks, an increasingly relevant model which can encode group…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
Graph rigidity, the study of vertex realizations in $\mathbb{R}^d$ and the motions that preserve the induced edge lengths, has been the focus of extensive research for decades. Its equivalency to graph connectivity for $d=1$ is well known;…
Two previous papers, arXiv:1803.00284 and arXiv:1803.00281, introduced and studied strong subgraph $k$-connectivity of digraphs obtaining characterizations, lower and upper bounds and computational complexity results for the new digraph…
Many of the structural characteristics of a network depend on the connectivity with and within the hubs. These dependencies can be related to the degree of a node and the number of links that a node shares with nodes of higher degree. In…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…