On the enhanced power graph of a semigroup
Web22 de jul. de 2024 · In this paper, we define and study the cyclic graph ΓS of a finite semigroup S. We obtain some graph theoretical properties of ΓS including its dominating … Web7 de fev. de 2024 · Sandeep Dalal, Jitender Kumar, Siddharth Singh, On the enhanced power graph of a semigroup, Algebra Colloquium (SCIE), Accepted . ... R.P. Panda, S. Dalal and J. Kumar, On the enhanced power graph of finite groups, Communications in Algebra (SCIE), 49(4):1697-1716, 2024. 9.
On the enhanced power graph of a semigroup
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WebThe enhanced power graph Γ G e of G is the graph with vertex set G and two distinct vertices are adjacent if they generate a cyclic subgroup of G. In this article, we calculate … WebThe purpose of this note is to prove that the chromatic number of $$\Gamma (S)$$ Γ ( S ) is at most countable. The present paper generalizes the results of Shitov (Graphs Comb 33(2):485–487, 2024) and the corresponding results on power graph and enhanced power graph of groups obtained by Aalipour et al. (Electron J Comb 24(3):#P3.16, 2024).
WebIn addition to enhanced power graph, other variants of power graphs have been considered recently, see [4, 6]. The cyclic graph of a semigroup S is a graph whose vertex set is S and two vertices u and v are adjacent if hu,vi = hwi for some w ∈ S. It can be observed that the notion of enhanced power graph and cyclic graph coincide when S is … 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
WebA 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}. Web27 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 …
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.
Web25 de jul. de 2024 · Published 25 July 2024. Mathematics. The enhanced power graph Pe (S) of a semigroup S is a simple graph whose vertex set is S and two vertices x, y ∈ S … stories beauty and the beast lyricsWeb31 de mar. de 2024 · Let G be a group. The power graph of G is a graph with vertex set G in which two distinct elements x, y are adjacent if one of them is a power of the other. We characterize all groups whose power graphs have finite independence number, show that they have clique cover number equal to their independence number, and calculate this … stories behind christmas hymnsWeb19 de out. de 2016 · This paper deals with the vertex connectivity of enhanced power graph of finite group. ... [33], power graph of a semigroup[18], deleted power graph of finite group[28], ... rose tree apts media paWebthe 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 rose treatments diseaseWebDefinition 2. The enhanced power graph GE(G) of a group G is the graph with vertex set G, and two vertices a and b are adjacent if and only if a,b ∈ hci, for some c ∈ G. Various properties of the enhanced power graph of finite groups have been stud-ied in detail. Aalipour et al. [3] characterized finite groups for which the power and stories beauty and the beastWeb17 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 … rose tree assisted living media paWebLet D be a directed graph. We say that an infinite semigroup 5 is power D-saturated if and only if, for every infinite subset T of 5, the power graph of S has a subgraph isomorphic … rose tree bridal