On the enhanced power graph of a semigroup
Web25 de jul. de 2024 · The enhanced power graph P e ( S) of a semigroup S is a simple graph whose vertex set is S and two vertices x, y ∈ S are adjacent if and only if x, y ∈ z for some z ∈ S, where z is the subsemigroup generated by z. In this paper, first we described the structure of P e ( S) for an arbitrary semigroup S. Consequently, we discussed the ... WebThe enhanced power graph Pe(S) of a semigroup S is a simple graph whose vertex set is S and two vertices x;y 2 S are adjacent if and only if x;y 2 hzi for some z 2 S, where hzi is …
On the enhanced power graph of a semigroup
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WebOn The Enhanced Power Graph of a Semigroup. S Dalal, J Kumar, S Singh. arXiv preprint arXiv:2107.11793, 2024. 2: 2024: The cyclic graph of a semigroup. S Dalal, J Kumar, S Singh. arXiv preprint arXiv:2107.11021, 2024. 2: 2024: On the Connectivity and Equality of Some Graphs on Finite Semigroups. Webthe power graph and the enhanced power graph of a group, arXiv 1603.04337. I Peter J. Cameron, The power graph of a finite group II, J. Group Theory 13 (2010), 779–783. I Peter J. Cameron, Andrea Lucchini and Colva M. Roney-Dougal, Generating sets of finite groups, arXiv 1609.06077. I A. V. Kelarev and S. J. Quinn, A combinatorial property
Web1 de mar. de 2024 · Abstract. The enhanced power graph of a finite group G, denoted by P_E (G), is a simple undirected graph whose vertex set is G and two distinct vertices x, y are adjacent if x, y \in \langle z \rangle for some z \in G. In this article, we determine all finite groups such that the minimum degree and the vertex connectivity of P_E (G) are equal. Web1 de mar. de 2024 · Search ACM Digital Library. Search Search. Advanced Search
Web8 de abr. de 2024 · We call this new graph as the \emph{enhanced power graph}. ... Undirected power graphs of semigroups, Semigroup Forum, 78 (2009), 410-426. Recommended publications. Discover more. Conference Paper. Web3 de jan. de 2024 · This paper deals with the vertex connectivity of enhanced power graphs of finite groups. We classify all abelian groups G such that the vertex …
Web1 de jul. de 2024 · Pub Date: July 2024 DOI: 10.48550/arXiv.2107.11793 arXiv: arXiv:2107.11793 Bibcode: 2024arXiv210711793D Keywords: Mathematics - Group Theory
Web[8] Sandeep Dalal, Jitender Kumar, Siddharth Singh, “On the Enhanced Power Graph of a Semigroup”, arXiv: 2107.11793v1[math.GR], 2024. [9] L. John and Padmakumari, “Semigroup Theoretic Study of Cayley graph of Rectangular Bands”, South East Asian Bulletin of Mathematics, vol. 35, pp. 943-950, 2010. inail renamWeb22 de jul. de 2024 · begin with an example of a semigroup whose cyclic graph and enhanced power graphs are not equal. Example 4.1. Let S = M (3 , 2) = { a, a 2 , a 3 , a … inail rhoWeb17 de out. de 2024 · Enhanced Power Graphs of Finite Groups. The enhanced power graph of a group is the graph with vertex set such that two vertices and are adjacent if they are contained in a same cyclic subgroup. We prove that finite groups with isomorphic enhanced power graphs have isomorphic directed power graphs. We show that any … inail lounge cactus las vegasWeb17 de out. de 2024 · Enhanced Power Graphs of Finite Groups. The enhanced power graph of a group is the graph with vertex set such that two vertices and are adjacent if … inail recupero passwordWeb27 de jan. de 2009 · 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 a … inail rho pecWeb1 de jun. de 2024 · In this paper it is proved that, if two groups have isomorphic power graphs, then they have isomorphic enhanced power graphs too. A sufficient condition … inail rumoreWebA rainbow path in an edge-colored graph G is a path that every two edges have different colors.The minimum number of colors needed to color the edges of G such that every two distinct vertices are connected by a rainbow path is called the rainbow connection number of G.Let (Γ, *) be a finite group with T Γ = {t ∈ Γ t ≠ t −1}. inail rx