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Sajal Kumar Mukherjee

Publications and source records attributed to Sajal Kumar Mukherjee.

5 recordsLinked to original sources
arXiv2020

On the connectivity of enhanced power graph of finite group

This paper deals with the vertex connectivity of enhanced power graph of finite group. We classify all abelian groups G such that vertex connectivity of enhanced power graph of G is 1. We derive an upper bound of vertex connectivity for the enhanced power graph of any general abelian group G. Also we completely characterize all abelian group G, such that the proper enhanced power graph is connected. Moreover, we study some special class of non-abelian group G such that the proper enhanced power graph is connected and we find their vertex connectivity.

math.CO↗
arXiv2020

Generalized power sum and Newton-Girard identities

In this article we prove an algebraic identity which significantly generalizes the formula for sum of powers of consecutive integers involving Stirling numbers of the second kind. Also we have obtained a generalization of Newton-Girard power sum identity.

math.CO↗
arXiv2018

Combinatorial proofs of the Newton-Girard and Chapman-Costas-Santos identities

In this paper we give combinatorial proofs of some well known identities and obtain some generalizations. We give a visual proof of a result of Chapman and Costas-Santos regarding the determinant of sum of matrices. Also we find a new identity expressing permanent of sum of matrices. Besides, we give a graphical interpretation of Newton-Girard identity.

math.CO↗
arXiv2016

On the power graph of the direct product of two groups

The power graph $P(G)$ of a finite group $G$ is the graph with vertex set $G$ and two distinct vertices are adjacent if either of them is a power of the other. Here we show that the power graph $P(G_1 \times G_2)$ of the direct product of two groups $G_1$ and $G_2$ is not isomorphic to either of the direct, cartesian and normal product of their power graphs $P(G_1)$ and $P(G_2)$. A new product of graphs, namely generalized product, has been introduced and we prove that the power graph $P(G_1 \times G_2)$ is isomorphic to a generalized product of $P(G_1)$ and $P(G_2)$.

math.CO↗