given a graph $g$, the total dominator coloring problem seeks aproper coloring of $g$ with the additional property that everyvertex in the graph is adjacent to all vertices of a color class. weseek to minimize the number of color classes. we initiate to studythis problem on several classes of graphs, as well as findinggeneral bounds and characterizations. we also compare the totaldominator chro...

we find recursive formulae for the number of perfect matchings in a graph g by splitting g into subgraphs h and q. we use these formulas to count perfect matching of p hypercube qn. we also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in g, is the graph constructed from by deleting edges with an en...

The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...

Throughout this paper, R will denote a commutative ring with identity and M is a unitary R- module and Z will denote the ring of integers. We introduce the graph Ω(M) of module M with the set of vertices contain all nontrivial non-essential submodules of M. We investigate the interplay between graph-theoretic properties of Ω(M) and algebraic properties of M. Also, we assign the values of natura...

An ef®cient system has been developed for the in vitro plant regeneration of Lilium longi ̄orum Thunb. by culturing receptacle sections from ̄ower buds. The sections were cultured on one-half MS medium plus 30 g lÿ1 sucrose, 8 g lÿ1 agar, 5.4 mM NAA or 4.9 mM IBA plus 2.2 mM BAP. A section size of 3±4 mm was found to be optimal. After 60 days an average of 41 shoots were formed per explant. More...

It has now been 30 years since the implantable cardioverterefibrillator (ICD) was introduced to the cardiovascular ommunity for the prevention of sudden cardiac death 1). Perhaps it is no longer common knowledge that the efibrillator was conceived and initially developed 40 ears ago by Drs. Michel Mirowski and Morton Mower, ot in an eminent medical institution with the robust upport of industry...

ower transformers and steam turbines were the key drivers in the development of the AC power system paradigm at the dawn of the 20th century, characterized by huge synchronous generators feeding millions of passive loads through large interconnected systems, all of them supervised and controlled from a centralized energy management system (EMS). In the same way, thyristor valves and IGBTs, intr...

let g = (v, e) be a simple graph. hosoya polynomial of g isd(u,v)h(g, x) = {u,v}v(g)x , where, d(u ,v) denotes the distance between vertices uand v. as is the case with other graph polynomials, such as chromatic, independence anddomination polynomial, it is natural to study the roots of hosoya polynomial of a graph. inthis paper we study the roots of hosoya polynomials of some specific graphs.

let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...