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Angsuman Das

Publications and source records attributed to Angsuman Das.

30 records · Page 2Linked to original sources
arXiv2022

On Co-Maximal Subgroup Graph of a Group

The co-maximal subgroup graph $Γ(G)$ of a group $G$ is a graph whose vertices are non-trivial proper subgroups of $G$ and two vertices $H$ and $K$ are adjacent if $HK=G$. In this paper, we continue the study of $Γ(G)$, especially when $Γ(G)$ has isolated vertices. We define a new graph $Γ^*(G)$, which is obtained by removing isolated vertices from $Γ(G)$. We characterize when $Γ^*(G)$ is connected, a complete graph, star graph, has an universal vertex etc. We also find various graph parameters like diameter, girth, bipartiteness etc. in terms of properties of $G$.

math.GR↗
arXiv2022

Determining Number of Kneser Graphs: Exact Values and Improved Bounds

The determining number of a graph $G = (V,E)$ is the minimum cardinality of a set $S\subseteq V$ such that pointwise stabilizer of $S$ under the action of $Aut(G)$ is trivial. In this paper, we provide some improved upper and lower bounds on the determining number of Kneser graphs. Moreover, we provide the exact value of the determining number for some subfamilies of Kneser graphs.

math.CO↗
arXiv2021

On Perfectness of Annihilating-Ideal Graph of $\mathbb{Z}_n$

The annihilating-ideal graph of a commutative ring $R$ with unity is defined as the graph $\mathbb{AG}(R)$ with the vertex set is the set of all non-zero ideals with non-zero annihilators and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ = 0$. Nikandish {\it et.al.} proved that $\mathbb{AG}(\mathbb{Z}_n)$ is weakly perfect. In this short paper, we characterize $n$ for which $\mathbb{AG}(\mathbb{Z}_n)$ is perfect.

math.CO↗
arXiv2020

A Family of Tetravalent Half-transitive Graphs

In this paper, we introduce a new family of graphs, $Γ(n,a)$. We show that it is an infinite family of tetravalent half-transitive Cayley graphs. Apart from that, we determine some structural properties of $Γ(n,a)$.

math.CO↗
arXiv2019

Classification of Cayley Rose Window Graphs

Rose window graphs are a family of tetravalent graphs, introduced by Steve Wilson. Following it, Kovacs, Kutnar and Marusic classified the edge-transitive rose window graphs and Dobson, Kovacs and Miklavic characterized the vertex transitive rose window graphs. In this paper, we classify the Cayley rose window graphs.

math.CO↗
arXiv2018

Triameter of Graphs

In this paper, we introduce and study a new distance parameter {\it triameter} of a connected graph $G$, which is defined as $max\{d(u,v)+d(v,w)+d(u,w): u,v,w \in V\}$ and is denoted by $tr(G)$. We find various upper and lower bounds on $tr(G)$ in terms of order, girth, domination parameters etc., and characterize the graphs attaining those bounds. In the process, we provide some lower bounds of (connected, total) domination numbers of a connected graph in terms of its triameter. The lower bound on total domination number was proved earlier by Henning and Yeo. We provide a shorter proof of that. Moreover, we prove Nordhaus-Gaddum type bounds on $tr(G)$ and find $tr(G)$ for some specific family of graphs.

math.CO↗
arXiv2017

Partial Domination in Graphs

Let $G=(V,E)$ be a graph. For some $α$ with $0<α\leq 1$, a subset $S$ of $V$ is said to be a $α$-partial dominating set if $|N[S]|\geq α|V|$. The size of a smallest such $S$ is called the $α$-partial domination number and is denoted by $\mathsf{pd}_α(G)$. In this paper, we introduce $α$-partial domination number in a graph $G$ and study different bounds on the partial domination number of a graph $G$ with respect to its order, maximum degree, domination number etc., Moreover, $α$-partial domination spectrum is introduced and Nordhaus-Gaddum bounds on the partial domination number are studied.

math.CO↗
arXiv2017

Subspace Sum Graph of a Vector Space

In this paper we introduce a graph structure, called subspace sum graph $\mathcal{G}(\mathbb{V})$ on a finite dimensional vector space $\mathbb{V}$ where the vertex set is the collection of non-trivial proper subspaces of a vector space and two vertices $W_1,W_2$ are adjacent if $W_1 + W_2=\mathbb{V}$. The diameter, girth, connectivity, maximal independent sets, different variants of domination number, clique number and chromatic number of $\mathcal{G}(\mathbb{V})$ are studied. It is shown that two subspace sum graphs are isomorphic if and only if the base vector spaces are isomorphic. Finally some properties of subspace sum graph are studied when the base field is finite.

math.CO↗
arXiv2016

Non-Zero Component Graph of a Finite Dimensional Vector Space

In this paper, we introduce a graph structure, called non-zero component graph on finite dimensional vector spaces. We show that the graph is connected and find its domination number and independence number. We also study the inter-relationship between vector space isomorphisms and graph isomorphisms and it is shown that two graphs are isomorphic if and only if the corresponding vector spaces are so. Finally, we determine the degree of each vertex in case the base field is finite.

math.GM↗
arXiv2015

On Non-Zero Component Graph of Vector Spaces over Finite Fields

In this paper, we study non-zero component graph $Γ(\mathbb{V})$ on a finite dimensional vector space $\mathbb{V}$ over a finite field $\mathbb{F}$. We show that the graph is Hamiltonian and not Eulerian. We also characterize the maximal cliques in $Γ(\mathbb{V})$ and show that there exists two classes of maximal cliques in $Γ(\mathbb{V})$. We also find the exact clique number of $Γ(\mathbb{V})$ for some particular cases. Moreover, we provide some results on size, edge-connectivity and chromatic number of $Γ(\mathbb{V})$.

math.GM↗
arXiv2011

An efficient multi-use multi-secret sharing scheme based on hash function

In this paper, a renewable, multi-use, multi-secret sharing scheme for general access structure based on one-way collision resistant hash function is presented in which each participant has to carry only one share. By applying collision-resistant one-way hash function, the proposed scheme is secure against conspiracy attacks even if the pseudo-secret shares are compromised. Moreover, high complexity operations like modular multiplication, exponentiation and inversion are avoided to increase its efficiency. Finally, in the proposed scheme, both the combiner and the participants can verify the correctness of the information exchanged among themselves.

cs.CR↗