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pro vyhledávání: '"Bera, Sudip"'
Autor:
Bera, Sudip
The enhanced power graph of a group G is a graph with vertex set G, where two distinct vertices x and y are adjacent if and only if there exists an element w in G such that both x and y are powers of w. To obtain the proper enhanced power graph, we c
Externí odkaz:
http://arxiv.org/abs/2407.06652
Autor:
Bera, Sudip, Dey, Hiranya Kishore
The enhanced power graph of a group $G$ is a graph with vertex set $G,$ where two distinct vertices $x$ and $y$ are adjacent if and only if there exists an element $w$ in $G$ such that both $x$ and $y$ are powers of $w.$ In this paper, we determine t
Externí odkaz:
http://arxiv.org/abs/2405.01027
Autor:
Bera, Sudip
Publikováno v:
Graphs and Combinatorics(2024)
In this paper, we introduce a matrix $A_{\Gamma_{k, R}}$ associate with a $k$-colored acyclic digraph $\Gamma_{k, R}$ such that $\text{det}(A_{\Gamma_{k, R}})$ enumerates the paths in the digraph $\Gamma_{k, R}.$
Comment: 11 pages, 3 figures. Ac
Comment: 11 pages, 3 figures. Ac
Externí odkaz:
http://arxiv.org/abs/2204.03367
Autor:
Bera, Sudip
We look for a non-zero $(0, 1)$-vector in the row space of the adjacency matrix $A(\Gamma)$ of a graph $\Gamma,$ provided $\Gamma$ has at least one edge. Akbari, Cameron, and Khosrovshahi conjectured that there exists a non-zero $(0,1)$-vector in the
Externí odkaz:
http://arxiv.org/abs/2204.02689
Autor:
Bera, Sudip, Dey, Hiranya Kishore
For a group $G,$ the enhanced power graph of $G$ is a graph with vertex set $G$ in which two distinct elements $x, y$ are adjacent if and only if there exists an element $w$ in $G$ such that both $x$ and $y$ are powers of $w.$ The proper enhanced pow
Externí odkaz:
http://arxiv.org/abs/2108.05175
Autor:
Bera, Sudip
Publikováno v:
Communications in Algebra, 2022
This paper deals with the classification of groups $G$ such that power graphs and proper power graphs of $G$ are line graphs. In fact, we classify all finite nilpotent groups whose power graphs are line graphs. Also, we categorize all finite nilpoten
Externí odkaz:
http://arxiv.org/abs/2104.06694
Autor:
Bera, Sudip
In this article we provide with combinatorial proofs of some recent identities due to Sury and McLaughlin. We show that, the solution of a general linear recurrence with constant coefficients can be interpreted as a determinant of a matrix. Also, we
Externí odkaz:
http://arxiv.org/abs/2009.06162
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
Externí odkaz:
http://arxiv.org/abs/2007.03217
Autor:
Bera, Sudip, Mukherjee, Sajal Kumar
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 iden
Externí odkaz:
http://arxiv.org/abs/2004.14590
Autor:
Bera, Sudip
In this article, we evaluate determinants of block hook matrices, which are block matrices consist of hook matrices. In particular, we deduce that the determinant of a block hook matrix factorizes nicely. In addition we give a combinatorial interpret
Externí odkaz:
http://arxiv.org/abs/1912.01338