B. K. Sahoo

activity

20062025

most citedVertex connectivity of the power graph of a finite cyclic group

19 citations · 26 across the 16 of their papers we have counts for

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14 papers · 1 filter

math.CO2025

On the minimum cut-sets of the power graph of a finite cyclic group, II

Sanjay Mukherjee, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph $P (G)$ of a finite group $G$ is the simple graph with vertex set $G$ and two distinct vertices are adjacent if one of them is a power of the other. Let $n…

math.CO2022★ 1 cited

On the minimum cut-sets of the power graph of a finite cyclic group

Sanjay Mukherjee, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph $P (G)$ of a finite group $G$ is the simple graph with vertex set $G$ , in which two distinct vertices are adjacent if one of them is a power of the other.…

math.CO2021

On the minimum degree of power graphs of finite nilpotent groups

Ramesh Prasad Panda, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph $P (G)$ of a group $G$ is the simple graph with vertex set $G$ and two vertices are adjacent whenever one of them is a positive power of the other. In this…

math.CO2020★ 1 cited

Proper divisor graph of a positive integer

Hitesh Kumar, Kamal Lochan Patra, Binod Kumar Sahoo

The proper divisor graph $Υ_{n}$ of a positive integer $n$ is the simple graph whose vertices are the proper divisors of $n$ , and in which two distinct vertices $u, v$ are adjacent i…

math.CO2019

On the minimum degree of the power graph of a finite cyclic group

Ramesh Prasad Panda, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph $P (G)$ of a finite group $G$ is the simple undirected graph whose vertex set is $G$ , in which two distinct vertices are adjacent if one of them is an inte…

math.CO2018

Vertex connectivity of the power graph of a finite cyclic group II

Sriparna Chattopadhyay, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph $P (G)$ of a given finite group $G$ is the simple undirected graph whose vertices are the elements of $G$ , in which two distinct vertices are adjacent if a…

math.CO2018

Minimal cut-sets in the power graphs of certain finite non-cyclic groups

Sriparna Chattopadhyay, Kamal Lochan Patra, Binod Kumar Sahoo

The power graph of a group is the simple graph with vertices as the group elements, in which two distinct vertices are adjacent if and only if one of them can be obtained as an int…

math.CO2017★ 19 cited

Vertex connectivity of the power graph of a finite cyclic group

Sriparna Chattopadhyay, Kamal Lochan Patra, Binod Kumar Sahoo

Let $n = p_{1}^{n_{1}} p_{2}^{n_{2}} \dots p_{r}^{n_{r}}$ , where $r, n_{1}, \dots, n_{r}$ are positive integers and $p_{1}, p_{2}, \dots, p_{r}$ are distinct prime numbers with $p_{1} < p_{2} < \dots < p_{r}$ . For the…

math.CO2010

Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth

Kamal Lochan Patra, Binod Kumar Sahoo

In this paper we consider the following problem: Over the class of all simple connected unicyclic graphs on $n$ vertices with girth $g$ ( $n, g$ being fixed), which graph minimizes t…

math.CO2010

Algebraic connectivity of connected graphs with fixed number of pendant vertices

Arbind K. Lal, Kamal L. Patra, Binod K. Sahoo

In this paper we consider the following problem: Over the class of all simple connected graphs of order $n$ with $k$ pendant vertices ( $n, k$ being fixed), which graph maximizes (re…

math.CO2010

Non-abelian representations of the slim dense near hexagons on 81 and 243 points

B. De Bruyn, B. K. Sahoo, N. S. N. Sastry

We prove that the near hexagon $Q (5, 2) \times L_{3}$ has a non-abelian representation in the extra-special 2-group $2_{+}^{1 + 12}$ and that the near hexagon $Q(5,2) \otimes Q(5…

math.CO2006★ 3 cited

On the order of a non-abelian representation group of a slim dense near hexagon

Binod Kumar Sahoo, N. S. Narasimha Sastry

We show that, if the representation group $R$ of a slim dense near hexagon $S$ is non-abelian, then $R$ is of exponent 4 and $∣ R ∣ = 2^{β}$ , $1 + N P d im (S) \leq β \leq 1 + d imV (S)$ , where $NPd…

math.CO2006★ 1 cited

New constructions of two slim dense near hexagons

Binod Kumar Sahoo

We provide a geometrical construction of the slim dense near hexagon with parameters $(s, t, t_{2}) = (2, 5, {1, 2})$ . Using this construction, we construct the rank 3 symplectic dual p…

math.CO2006

On the existence of non-abelian representations of slim dense near hexagons having big quads

Binod Kumar Sahoo, N. S. Narasimha Sastry

This paper has been withdrawn as the statements in Proposition 4.4 and Theorem 1.4(i) are not correct.