Subhabrata Paul

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20232025

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6 papers · 1 filter

math.CO2025

Liar's vertex-edge domination in unit disk graph

Debojyoti Bhattacharya, Subhabrata Paul

Let $G = (V, E)$ be a simple undirected graph. A closed neighbourhood of an edge $e = uv$ between two vertices $u$ and $v$ of $G$ , denoted by $N_{G} [e]$ , is the set of vertices in the ne…

math.CO2025

Liar's vertex-edge domination in subclasses of chordal graphs

Debojyoti Bhattacharya, Subhabrata Paul

Let $G = (V, E)$ be an undirected graph. The set $N_{G} [x] = {y \in V ∣ x y \in E} \cup {x}$ is called the closed neighbourhood of a vertex $x \in V$ and for an edge $e = x y \in E$ , the closed…

math.CO2024

On the Complexity and Algorithms for the Upper Domatic Number of Graphs

Subhabrata Paul, Kamal Santra

Let $G$ be a graph. For two disjoint vertex sets $A,B\subseteq V(G)$, we say that $A$ dominates $B$ if every vertex of $B$ has a neighbour in $A$. An upper domatic part…

math.CO2023

On $k$ -vertex-edge domination of graph

Debojyoti Bhattacharya, Subhabrata Paul

Let $G = (V, E)$ be a simple undirected graph. The open neighbourhood of a vertex $v$ in $G$ is defined as $N_{G} (v) = {u \in V ∣ uv \in E}$ ; whereas the closed neighbourhood is defined…

math.CO2023

Strong transitivity of a graph

Subhabrata Paul, Kamal Santra

A vertex partition $π = {V_{1}, V_{2}, \dots, V_{k}}$ of $G$ is called a \emph{transitive partition} of size $k$ if $V_{i}$ dominates $V_{j}$ for all $1 \leq i < j \leq k$ . For two disjoint su…

math.CO2023

Algorithmic study on $2$ -transitivity of graphs

Subhabrata Paul, Kamal Santra

Let $G = (V, E)$ be a graph where $V$ and $E$ are the vertex and edge sets, respectively. For two disjoint subsets $A$ and $B$ of $V$ , we say $A$ \emph{dominates} $B$ if every vertex…

Liar's vertex-edge domination in unit disk graph

Liar's vertex-edge domination in subclasses of chordal graphs

On the Complexity and Algorithms for the Upper Domatic Number of Graphs

On k-vertex-edge domination of graph

Strong transitivity of a graph

Algorithmic study on 2-transitivity of graphs

On $k$ -vertex-edge domination of graph

Algorithmic study on $2$ -transitivity of graphs