相关论文: On global offensive k-alliances in graphs
For a finite group $G$ and for a fixed positive integer $k$, $k\geq 2$, the $k$-power graph of $G$ is an undirected simple graph with vertex set $G$ in which two distinct vertices $x$ and $y$ are adjacent if and only if $x^k=y$ or $y^k=x$.…
We give a sharp lower bound on the lower $k$-limited packing number of a general graph. Moreover, we establish a Nordhaus-Gaddum type bound on $2$-limited packing number of a graph. Also, we investigate the concepts of packing number…
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…
This paper investigates some relationship between the algebraic connectivity and the clique number of graphs. We characterize all extremal graphs which have the maximum and minimum the algebraic connectivity among all graphs of order $n$…
We prove that, in games in which all the guards move at the same turn, the eternal domination and the clique-connected cover numbers coincide for interval graphs. A linear algorithm for the eternal dominating set problem is obtained as a…
A generalization of G-sets, called partial G-sets, are the sets that admit an action of partial maps on their subsets. Partial actions are a powerful tool to generalize many results of group actions. These generalizations are obtained by…
We study the m-Eternal Domination problem, which is the following two-player game between a defender and an attacker on a graph: initially, the defender positions k guards on vertices of the graph; the game then proceeds in turns between…
In this paper we give a new generalization of token graphs. Given two integers $1\leq m \leq k$ and a graph $G$ we define the generalized token graph of the graph $G$, to be the graph $F_k^m(G)$ whose vertices correspond to configurations…
A defensive alliance in an undirected graph $G=(V,E)$ is a non-empty set of vertices $S$ satisfying the condition that every vertex $v\in S$ has at least as many neighbours (including itself) in $S$ as it has in $V\setminus S$. We consider…
A subset $D$ of vertices of a graph $G$ is a \textit{dominating set} if for each $u\in V(G)\setminus D$, $u$ is adjacent to some vertex $v\in D$. The \textit{dominating number}, $\gamma(G)$ of $G$, is the minimum cardinality of a dominating…
The $k$-rainbow domination problem is studied for regular graphs. We prove that the $k$-rainbow domination number $\gamma_{rk}(G)$ of a $d$-regular graph for $d\leq k\leq 2d$ is bounded below by $\displaystyle{\left\lceil…
This work focuses on developing an effective meta-heuristic approach to protect against simultaneous attacks on nodes of a network modeled using a graph. Specifically, we focus on the $k$-strong Roman domination problem, a generalization of…
The $k$-power domination problem is a problem in graph theory, which has applications in many areas. However, it is hard to calculate the exact $k$-power domination number since determining k-power domination number of a generic graph is a…
We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of…
We define and investigate properties of universal operator algebras of directed graphs. Results include free products decomposition and continuity of the construction with respect to direct limits. Lastly we prove some K-theoretic results…
A $k$-uniform hypergraph with $n$ vertices is an $(n,k,\ell)$-omitting system if it does not contain two edges whose intersection has size exactly $\ell$. If in addition it does not contain two edges whose intersection has size greater than…
We give an efficient construction of a reasonably small dominating set in a circulant graph on $n$ notes and $k$ distinct chord lengths. This result is based on bounds on some double exponential sums. .
In communication networks, the binding numbers of graphs (or networks) are often used to measure the vulnerability and robustness of graphs (or networks). Furthermore, the fractional factors of graphs and the fractional…
A well-known result of Alon shows that the coloring number of a graph is bounded by a function of its choosability. We explore this relationship in a more general setting with relaxed assumptions on color classes, encoded by a graph…
Due to the increasing discovery and implementation of networks within all disciplines of life, the study of subgraph connectivity has become increasingly important. Motivated by the idea of community (or sub-graph) detection within a…