Author
Shamik Ghosh
Other affiliations: University of Calcutta, Scottish Church College
Bio: Shamik Ghosh is an academic researcher from Jadavpur University. The author has contributed to research in topics: Chordal graph & Interval graph. The author has an hindex of 8, co-authored 32 publications receiving 741 citations. Previous affiliations of Shamik Ghosh include University of Calcutta & Scottish Church College.
Papers
More filters
TL;DR: In this article, it was shown that the multiplicative semigroup ℤn and its subgroup Un is complete if and only if n = 1,2,4,p or 2p, where p is a Fermat prime.
Abstract: The undirected power graph G(S) of a semigroup S is an undirected graph whose vertex set is S and two vertices a,b∈S are adjacent if and only if a≠b and am=b or bm=a for some positive integer m. In this paper we characterize the class of semigroups S for which G(S) is connected or complete. As a consequence we prove that G(G) is connected for any finite group G and G(G) is complete if and only if G is a cyclic group of order 1 or pm. Particular attention is given to the multiplicative semigroup ℤn and its subgroup Un, where G(Un) is a major component of G(ℤn). It is proved that G(Un) is complete if and only if n=1,2,4,p or 2p, where p is a Fermat prime. In general, we compute the number of edges of G(G) for a finite group G and apply this result to determine the values of n for which G(Un) is planar. Finally we show that for any cyclic group of order greater than or equal to 3, G(G) is Hamiltonian and list some values of n for which G(Un) has no Hamiltonian cycle.
266 citations
TL;DR: It is conjectured that two finite groups with isomorphic power graphs have the same number of elements of each order, and that the only finite group whose automorphism group is the same as that of its power graph is the Klein group of order 4.
225 citations
TL;DR: The intersection graph G(R) of nontrivial left ideals of a ring R is considered, and the values of n for which G(Z"n) is connected, complete, bipartite, planar or has a cycle are determined.
139 citations
TL;DR: The intersection graph G(R) of nontrivial left ideals of a ring R is considered, which is a set of all non-isomorphic graphs of Z n for a given number of vertices.
63 citations
TL;DR: The aim of this paper is to characterize prime fuzzy k-ideals, semiregular semirings, NoetherianSemirings and Artinian Semirings by fuzzy k -ideals.
61 citations
Cited by
More filters
[...]
TL;DR: This paper initiates the study of soft semirings by using the soft set theory, and the notions of soft Semirings, soft subsemirings,soft ideals, idealistic softSemirings and soft semiring homomorphisms are introduced, and several related properties are investigated.
Abstract: Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft semirings by using the soft set theory. The notions of soft semirings, soft subsemirings, soft ideals, idealistic soft semirings and soft semiring homomorphisms are introduced, and several related properties are investigated.
579 citations
TL;DR: It is conjectured that two finite groups with isomorphic power graphs have the same number of elements of each order, and that the only finite group whose automorphism group is the same as that of its power graph is the Klein group of order 4.
225 citations
13 Nov 2013
TL;DR: This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature.
Abstract: This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature. Various conjectures due to other authors, questions and open problems are also included.
187 citations
01 May 2017
TL;DR: The concept of soft rough hemirings is introduced, which is an extended notion of a rough hemiring, which provides a new research idea for soft rough algebraic research.
Abstract: Graphical abstractDisplay Omitted In this paper, we investigate the relationships among rough sets, soft sets and hemirings. The concept of soft rough hemirings is introduced, which is an extended notion of a rough hemiring. It is pointed out that in this paper, we first apply soft rough sets to algebraic structure-hemirings. Further, we first put forward the concepts of C-soft sets and CC-soft sets, which provide a new research idea for soft rough algebraic research. Moreover, we study roughness in hemirings with respect to MSR-approximation spaces. Some new soft rough operations over hemirings are explored. In particular, lower and upper MSR-hemirings (k-ideal and h-ideal) are investigated. Finally, we put forth an approach for multicriteria group decision making problem based on modified soft rough sets and offer an actual example.
158 citations
01 Jan 2011
TL;DR: A survey of the recent and active area of zero-divisor graphs of commutative rings can be found in this paper, followed by a historical overview and an extensive bibliography.
Abstract: This article surveys the recent and active area of zero-divisor graphs of commutative rings. Notable algebraic and graphical results are given, followed by a historical overview and an extensive bibliography.
153 citations