Related papers: On global offensive k-alliances in graphs

The independent domination number $i(G)$ of a graph $G$ is the minimum cardinality of a maximal independent set of $G$, also called an $i(G)$-set. The $i$-graph of $G$, denoted $\mathcal{I}(G)$, is the graph whose vertices correspond to the…

A set $S$ of vertices in a graph $G$ is a dominating set if every vertex of $G$ is in $S$ or is adjacent to a vertex in $S$. If, in addition, $S$ is an independent set, then $S$ is an independent dominating set. The domination number…

In a graph $G$, a vertex dominates itself and its neighbours. A set $D\subseteq V(G)$ is said to be a $k$-tuple dominating set of $G$ if $D$ dominates every vertex of $G$ at least $k$ times. The minimum cardinality among all $k$-tuple…

A dominating set in a graph is a set of vertices with the property that every vertex in the graph is either in the set or adjacent to something in the set. The domination sequence of the graph is the sequence whose $k$th term is the number…

We initiate the study of computational problems on $k$-mers (strings of length $k$) in labeled graphs. As a starting point, we consider the problem of counting the number of distinct $k$-mers found on the walks of a graph. We establish that…

Random K-out graphs are garnering interest in designing distributed systems including secure sensor networks, anonymous crypto-currency networks, and differentially-private decentralized learning. In these security-critical applications, it…

This paper investigates the class of k-universal finite graphs, a local analog of the class of universal graphs, which arises naturally in the study of finite variable logics. The main results of the paper, which are due to Shelah,…

Deep neural networks (DNNs) have been widely applied to various applications, including image classification, text generation, audio recognition, and graph data analysis. However, recent studies have shown that DNNs are vulnerable to…

Real social network datasets provide significant benefits for understanding phenomena such as information diffusion or network evolution. Yet the privacy risks raised from sharing real graph datasets, even when stripped of user identity…

A graph $G$ is a $D\!D_2$-graph if it has a pair $(D,D_2)$ of disjoint sets of vertices of $G$ such that $D$ is a dominating set and $D_2$ is a 2-dominating set of $G$. We provide several characterizations and hardness results concerning…

We generalize the concept of token graphs to obtain supertoken graphs. In the latter case, there can be more than one token in a vertex. We formally define supertoken graphs and establish their basic properties. Moreover, we provide some…

Deep learning models on graphs have achieved remarkable performance in various graph analysis tasks, e.g., node classification, link prediction, and graph clustering. However, they expose uncertainty and unreliability against the…

We determine the maximum possible number of edges of a graph with $n$ vertices, matching number at most $s$ and clique number at most $k$ for all admissible values of the parameters.

Different variations of alliances in graphs have been introduced into the graph-theoretic literature about twenty years ago. More broadly speaking, they can be interpreted as groups that collaborate to achieve a common goal, for instance,…

We discuss the close relationship between structural theorems in generalized stability theory and graph regularity theorems.

We present new greedy and beam search heuristic methods to find small-size $k$-dominating sets in graphs. The methods are inspired by a new problem formulation which explicitly highlights a certain structure of the problem. An empirical…

We study the problem of maximizing the number of independent sets in $n$-vertex $k$-chromatic $\ell$-connected graphs. First we consider maximizing the total number of independent sets in such graphs with $n$ sufficiently large, and for…

We introduce a new notion of resilience for constraint satisfaction problems, with the goal of more precisely determining the boundary between NP-hardness and the existence of efficient algorithms for resilient instances. In particular, we…

We study the set of all determinants of adjacency matrices of graphs with a given number of vertices.

For an ordered set $W=\{w_1,w_2,...,w_k\}$ of vertices and a vertex $v$ in a connected graph $G$, the ordered $k$-vector $r(v|W):=(d(v,w_1),d(v,w_2),...,d(v,w_k))$ is called the (metric) representation of $v$ with respect to $W$, where…