ARTICLE
TITLE

Index graphs of finite permutation groups

SUMMARY

Let G be a subgroup of Sn. For x ? G, the index of x in G is denoted by ind x is the minimal number of 2-cycles needed to express x as a product. In this paper, we define a new kind of graph on G, namely the index graph and denoted by Gind(G). Its vertex set the set of all conjugacy classes of G and two distinct vertices x ? Cx and y ? Cy are adjacent if Gcd(ind x, ind y) 6 ? 1. We study some properties of this graph for the symmetric groups Sn, the alternating group An, the cyclic group Cn, the dihedral group D2n and the generalized quaternain group Q4n. In particular, we are interested in the connectedness of them.

PAGES
pp. 97 - 104

 Articles related

Süleyman Ediz    

Reduced second Zagreb index has been defined recently. In this paper we characterized extremal bicyclic graphs with pendent vertices with respect to this novel index.

Revista: Le Matematiche

Elliot Krop,Sin-Min Lee,Christopher Raridan    

We characterize strongly edge regular product graphs and find the edge-balanced index sets of complete bipartite graphs without a perfect matching, the direct product K<sub>n</sub> X K<sub>2</sub>. We also prove a lemma that is h... see more


Hanyuan Deng,Selvaraj Balachandran,Suresh Elumalai,Toufik Mansour    

Let G be a connected graph with vertex set V(G). The Harary index of a graph is defined as H(G) = ?u ? v 1/d(u, v), where d(u, v) denotes the distance between u and v. In this paper, we determine the extremal graphs with the maximum Harary index among al... see more


Ramin Nasiri,Hamid Reza Ellahi,Gholam Hossein Fath-Tabar,Ahmad Gholami    

The signless Laplacian Estrada index of a graph G is defined as SLEE(G) = ?ni = 1eqi where q1, q2, …, qn are the eigenvalues of the signless Laplacian matrix of G. Following the previous work in which we have identified the unique graphs with maximum sig... see more


Suresh Elumalai,Toufik Mansour,Mohammad Ali Rostami    

The hyper-Zagreb index of a simple connected graph G is defined by ?2(G) = ?uv ? E(G)(d(u) + d(v))2. In this paper, we establish, analyze and compare some new upper bounds on the Hyper-Zagreb index in terms of the number of vertices n, number of edges m,... see more