Zekhaya B. Shozi

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20232026

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8 papers · 1 filter

math.CO2026

Ratio of the number of $1$ -nearly independent vertex subsets and the Merrifield-Simmons index

Audace A. V. Dossou-Olory, Eric O. D. Andriantiana, Valisoa R. M. Rakotonarivo +1

The number $σ_{k} (G)$ of induced subgraphs with size $k$ of a graph $G$ was introduced recently as the number of $k$ -nearly independent vertex subsets of $G$ . Results highlighting si…

math.CO2026

Nordhaus-Gaddum inequalities for the number of 1-nearly independent vertex subsets

Eric O. D. Andriantiana, Zekhaya B. Shozi

For a graph $G$ , a vertex subset is called \emph{ $1$ -nearly independent} if the subgraph it induces contains exactly one edge. Let $σ_{1} (G)$ denote the number of such subsets in $G$ …

math.CO2025

On the generator graph of a cyclic group

Zekhaya B. Shozi, Teresa L. Tacbobo

In this paper, we continue the study of the generator graph of a group. In 2023, Tacbobo [9] defined the generator graph of a nontrivial group to be the graph whose vertices are th…

math.CO2024

An improved lower bound on the number of $1$ -nearly independent vertex subsets

Zekhaya B. Shozi

Let $G = (V (G), E (G))$ be a graph with set of vertices $V (G)$ and set of edges $E (G)$ . For $k \geq 0$ an integer, a subset $I_{k}$ of $V (G)$ is called a $k$ -nearly independent vertex subs…

math.CO2024

The $1$ -nearly edge independence number of a graph

Zekhaya B. Shozi

Let $G = (V (G), E (G))$ be a graph. The maximum cardinality of a set $M_{k} \subseteq E (G)$ such that $M_{k}$ contains exactly $k$ -pairs of adjacent edges of $G$ is called the $k$ -nearl…

math.CO2024

The $1$ -nearly vertex independence number of a graph

Zekhaya B. Shozi

Let $G$ be a graph with vertex set $V (G)$ and edge set $E (G)$ . A set $I_{0} (G) \subseteq V (G)$ is a vertex independent set if no two vertices in $I_{0} (G)$ are adjacent in $G$ . We stud…

math.CO2024

The number of 1-nearly independent edge subsets

Eric O. D. Andriantiana, Zekhaya B. Shozi

Let $G = (V (G), E (G))$ be a graph with set of vertices $V (G)$ and set of edges $E (G)$ . A subset $S$ of $E (G)$ is called a $k$ -nearly independent edge subsets if there are exactly $k$ …

math.CO2023

The number of $1$ -nearly independent vertex subsets

Eric Ould Dadah Andriantiana, Zekhaya B. Shozi

Let $G$ be a graph with vertex set $V (G)$ and edge set $E (G)$ . A subset $I$ of $V (G)$ is an independent vertex subset if no two vertices in $I$ are adjacent in $G$ . We study the nu…

Ratio of the number of 1-nearly independent vertex subsets and the Merrifield-Simmons index

Nordhaus-Gaddum inequalities for the number of 1-nearly independent vertex subsets

On the generator graph of a cyclic group

An improved lower bound on the number of 1-nearly independent vertex subsets

The 1-nearly edge independence number of a graph

The 1-nearly vertex independence number of a graph

The number of 1-nearly independent edge subsets

The number of 1-nearly independent vertex subsets

Ratio of the number of $1$ -nearly independent vertex subsets and the Merrifield-Simmons index

An improved lower bound on the number of $1$ -nearly independent vertex subsets

The $1$ -nearly edge independence number of a graph

The $1$ -nearly vertex independence number of a graph

The number of $1$ -nearly independent vertex subsets