Explanipedia

Complementary coalition graphs: characterization and algorithm Open

Davood Bakhshesh, Michael A. Henning · 2024

$k$-Coalitions in Graphs Open

Abbas Jafari, ‎Saeid Alikhani, Davood Bakhshesh · 2024

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 th…

Counting the Number of Domatic Partition of a Graph Open

‎Saeid Alikhani, Davood Bakhshesh, Nima Ghanbari · 2024

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 n…

On independent coalition in graphs and independent coalition graphs Open

‎Saeid Alikhani, Davood Bakhshesh, Hamidreza Golmohammadi, Sandi Klavžar · 2024

An independent coalition in a graph G consists of two disjoint, indepen-either the set V i consists of a single dominating vertex of G, or V i forms an independent coalition with some other part V j .The independent coalition number IC(G) …

Connected coalitions in graphs Open

‎Saeid Alikhani, Davood Bakhshesh, Hamidreza Golmohammadi, Elena V. Konstantinova · 2023

Let G = (V, E) be a graph, and define a connected coalition as a pair of disjoint vertex sets U 1 and U 2 such that U 1 ∪ U 2 forms a connected dominating set, but neither U 1 nor U 2 individually forms a connected dominating set.A connect…

Angle-monotonicity of theta-graphs for points in convex position Open

Davood Bakhshesh, Mohammad Farshi · 2023

For $0<\gamma<180^{\circ}$, a geometric path $P=(p_1,\ldots, p_n)$ is called angle-monotone with width $\gamma$ from $p_1$ to $p_n$ if there exists a closed wedge of angle $\gamma$ such that every directed edge $\overrightarrow{p_ip_{i+1}}…

The minmin coalition number in graphs Open

Davood Bakhshesh, Michael A. Henning · 2023

A set $S$ of vertices in a graph $G$ is a dominating set if every vertex of $V(G) \setminus S$ is adjacent to a vertex in $S$. A coalition in $G$ consists of two disjoint sets of vertices $X$ and $Y$ of $G$, neither of which is a dominatin…

Singleton Coalition Graph Chains Open

Davood Bakhshesh, Michael A. Henning, Dinabandhu Pradhan · 2023

Let $G$ be graph with vertex set $V$ and order $n=|V|$. A coalition in $G$ is a combination of two distinct sets, $A\subseteq V$ and $B\subseteq V$, which are disjoint and are not dominating sets of $G$, but $A\cup B$ is a dominating set o…

Connected coalitions in graphs Open

‎Saeid Alikhani, Davood Bakhshesh, Hamidreza Golmohammadi, Elena V. Konstantinova · 2023

The connected coalition in a graph $G=(V,E)$ consists of two disjoint sets of vertices $V_{1}$ and $V_{2}$, neither of which is a connected dominating set but whose union $V_{1}\cup V_{2}$, is a connected dominating set. A connected coalit…

Complementary Coalition Graphs: Characterization and Algorithm Open

Davood Bakhshesh · 2023

A lower bound on the stretch factor of Yao graph Y4 Open

Davood Bakhshesh, Mohammad Farshi · 2022

On the coalition number of trees Open

Davood Bakhshesh, Dinabandhu Pradhan · 2021

Let $G$ be a graph with vertex set $V$ and of order $n = |V|$, and let $δ(G)$ and $Δ(G)$ be the minimum and maximum degree of $G$, respectively. Two disjoint sets $V_1, V_2 \subseteq V$ form a coalition in $G$ if none of them is a dominati…

On the coalition number of graphs Open

Davood Bakhshesh, Dinabandhu Pradhan · 2021

Let $G$ be a graph with vertex set $V$. Two disjoint sets $V_1, V_2 \subseteq V$ form a coalition in $G$ if none of them is a dominating set of $G$ but their union $V_1\cup V_2$ is. A vertex partition $\Psi=\{V_1,\ldots, V_k\}$ of $V$ is c…

A Degree 3 Plane $5.19$-Spanner for Points in Convex Position Open

Davood Bakhshesh, Mohammad Farshi · 2021

Let $S$ be a set of $n$ points in the plane that is in convex position. In this paper, using the well-known path-greedy spanner algorithm, we present an algorithm that constructs a plane $frac{3+4pi}{3}$-spanner $G$ of degree 3 on the poin…

Continuous Yao graphs Open

Davood Bakhshesh, Luis Barba, Prosenjit Bose, Jean-Lou De Carufel, Mirela Damian , et al. · 2017

Complexity results for $k$-domination and $α$-domination problems and their variants Open

Davood Bakhshesh, Mohammad Farshi, Mahdieh Hasheminezhad · 2017

Let $G=(V, E)$ be a simple and undirected graph. For some integer $k\geq 1$, a set $D\subseteq V$ is said to be a k-dominating set in $G$ if every vertex $v$ of $G$ outside $D$ has at least $k$ neighbors in $D$. Furthermore, for some real …

Complexity results for $k$-domination and $\\alpha$-domination problems\n and their variants Open

Davood Bakhshesh, Mohammad Farshi, Mahdieh Hasheminezhad · 2017

Let $G=(V, E)$ be a simple and undirected graph. For some integer $k\\geq 1$,\na set $D\\subseteq V$ is said to be a k-dominating set in $G$ if every vertex\n$v$ of $G$ outside $D$ has at least $k$ neighbors in $D$. Furthermore, for some\n…

Some Properties of Continuous Yao Graph Open

Davood Bakhshesh, Mohammad Farshi · 2016

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