Zobrazeno 1 - 10
of 355
pro vyhledávání: '"Alikhani, Saeid"'
In this paper, we propose and investigate the concept of $k$-coalitions in graphs, where $k\ge 1$ is an integer. A $k$-coalition refers to a pair of disjoint vertex sets that jointly constitute a $k$-dominating set of the graph, meaning that every ve
Externí odkaz:
http://arxiv.org/abs/2407.09332
Autor:
Alikhani, Saeid, Ghanbari, Nima
Much has been written about the golden ratio $\phi=\frac{1+\sqrt{5}}{2}$ and this strange number appears mysteriously in many mathematical calculations. In this article, we review the appearance of this number in the graph theory. More precisely, we
Externí odkaz:
http://arxiv.org/abs/2407.15860
A subset of vertices $S$ of a graph $G$ is a dominating set if every vertex in $V \setminus S$ has at least one neighbor in $S$. A domatic partition is a partition of the vertices of a graph $G$ into disjoint dominating sets. The domatic number $d(G)
Externí odkaz:
http://arxiv.org/abs/2407.00103
Let $G$ be a simple graph with vertex set $V(G) = \{v_1, v_2,\ldots, v_n\}$. The elliptic Sombor matrix of $G$, denoted by $A_{ESO}(G)$, is defined as the $n\times n$ matrix whose $(i,j)$-entry is $(d_i+d_j)\sqrt{d_i^2+d_j^2}$ if $v_i$ and $v_j$ are
Externí odkaz:
http://arxiv.org/abs/2404.18622
Autor:
Alikhani, Saeid, Aghaei, Fatemeh
The domination polynomial (the total domination polynomial) of a graph $ G $ of order $ n $ is the generating function of the number of dominating sets (total dominating sets) of $ G $ of any size. In this paper, we study the domination polynomial an
Externí odkaz:
http://arxiv.org/abs/2404.13539
For a graph $G=(V,E)$, a set $D\subset V(G)$ is a strong dominating set of $G$, if for every vertex $x\in V (G)\setminus D$ there is a vertex $y\in D$ with $xy \in E(G)$ and $deg(x)\leq deg(y)$. A strong coalition consists of two disjoint sets of ver
Externí odkaz:
http://arxiv.org/abs/2404.11575
Autor:
Alikhani, Saeid, Aghaei, Fatemeh
Let $G=(V,E)$ be a simple graph. A function $\phi:V\rightarrow \mathbb{N}\cup \{0\}$ is called a configuration of pebbles on the vertices of $G$ and the quantity $\sum_{u\in V}\phi(u)$ is called the size of $\phi$ which is just the total number of pe
Externí odkaz:
http://arxiv.org/abs/2402.10017
Autor:
Taheri, Abbas, Alikhani, Saeid
A number $\alpha$ has a representation with respect to the numbers $\alpha_1,...,\alpha_n$, if there exist the non-negative integers $\lambda_1,... ,\lambda_n$ such that $\alpha=\lambda_1\alpha_1+...+\lambda_n \alpha_n$. The largest natural number th
Externí odkaz:
http://arxiv.org/abs/2402.07853
Autor:
Aghaei, Fatemeh, Alikhani, Saeid
Let $G=(V,E)$ be a simple graph. A function $f:V\rightarrow \mathbb{N}\cup \{0\}$ is called a configuration of pebbles on the vertices of $G$ and the quantity $\vert f\vert=\sum_{u\in V}f(u)$ is called the weight of $f$ which is just the total number
Externí odkaz:
http://arxiv.org/abs/2401.08528
A non-empty set $S\subseteq V (G)$ of the simple graph $G=(V(G),E(G))$ is an independent dominating set of $G$ if every vertex not in $S$ is adjacent with some vertex in $S$ and the vertices of $S$ are pairwise non-adjacent. The independent dominatio
Externí odkaz:
http://arxiv.org/abs/2311.01733