WebThe power graph of a group G is a simple graph whose vertex-set is G and two vertices x and y in G are adjacent if and only if one of them is a power of the other. The subgraph of is obtained by deleting the vertex 1 (the identity element of G). In this paper, we first investigate some properties of the power graph and its subgraph . Webis the finite cyclic group of order and the set consists of two elements, the standard generator of and its inverse, then the Cayley graph is the cycle . More generally, the Cayley graphs of finite cyclic groups are exactly the circulant graphs.
Cayley graph - Wikipedia
WebMar 9, 2024 · A finite group 𝐺 is normally monomial if all its irreducible characters are induced from linear characters of normal subgroups of 𝐺. ... then a certain graph associated to its conjugacy class that we call the star graph is either disconnected or has a cut vertex. ... In recent work, Cameron, Manna and Mehatari have studied the finite ... WebMar 26, 2024 · The inverse graph associated with as the graph whose vertex set coincides with such that two different vertices and are adjacent iff either or . When is the cyclic group and is the set of non-self-inverse … can asthma cause panic attacks
[2101.00363] The Prime Graphs of Some Classes of Finite Groups
WebFeb 19, 2024 · All groups considered in the present paper are supposed to be finite. The solubility graph \Gamma _S (G) associated with a group G is a simple graph whose vertices are the elements of G , and there is an edge between two distinct elements x and y if and only if the subgroup \langle x,y \rangle is soluble. WebDec 31, 2024 · The power graph P(G) of a finite group G is the graph whose vertex set isG, with two elements in G being adjacent if one of them is a power of theother. The purpose of this paper is twofold: (1) to find the complexity ofa clique-replaced graph and study some applications; (2) to derive someexplicit formulas concerning the complexity … WebJun 1, 2024 · Spectrum of a finite graph is defined as collection of all distinct eigenvalues and their algebraic multiplicity of its matrix. The most related topic in the study of spectrum of finite graph is energy. Energy of a finite graph is defined as sum of … can asthma cause pain between shoulder blades