abstract. in this paper we study some relations between the power andquotient power graph of a finite group. these interesting relations motivateus to find some graph theoretical properties of the quotient power graphand the proper quotient power graph of a finite group g. in addition, weclassify those groups whose quotient (proper quotient) power graphs areisomorphic to trees or paths.

in recent years wireless sensor networks have attracted researchers' attention due to vast applications. one of the most prominent issues regarding these networks is coverage which is considered as a quality of service parameter. in this study, we try to address energy shortage in wsns through finding a set of optimal coverage nodes in a specific environment. this is performed utilizing effecti...

a multicone graph is defined to be join of a clique and a regular graph. a graph $ g $ is  cospectral with  graph $ h $ if their adjacency matrices have the same eigenvalues. a graph $ g $ is  said to be  determined by its spectrum or ds for short, if for any graph $ h $ with $ spec(g)=spec(h)$, we conclude that $ g $ is isomorphic to $ h $. in this paper, we present new classes of  multicone g...

topological indices are the numerical value associated with chemical constitution purporting for correlation ofchemical structure with various physical properties, chemical reactivity or biological activity. graph theory is adelightful playground for the exploration of proof techniques in discrete mathematics and its results haveapplications in many areas of sciences. one of the useful indices ...

The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian matrix of G and average degree of the vertices of G. Motivated by the work from Sharafdini et al. [R. Sharafdini, H. Panahbar, Vertex weighted...

The purpose of this paper is the study of Cayley graph associated to a semihypergroup(or hypergroup). In this regards first  we associate a Cayley graph to every semihypergroup and then we study theproperties of this graph, such as  Hamiltonian cycles in this  graph.  Also, by some of examples we will illustrate  the properties and behavior of  these Cayley  graphs, in particulars we show that ...

let g be a fixed element of a finite group g. we introduce the g-noncommuting graph of g whose vertex set is whole elements of the group g and two vertices x,y are adjacent whenever [x,y] g  and  [y,x] g. we denote this graph by . in this paper, we present some graph theoretical properties of g-noncommuting graph. specially, we investigate about its planarity and regularity, its clique number a...