Let e be an edge of a G connecting the vertices u and v. Define two sets N1 (e | G) and N2(e |G) as N1(e | G)= {xV(G) d(x,u) d(x,v)} and N2(e | G)= {xV(G) d(x,v) d(x,u) }.The number of elements of N1(e | G) and N2(e | G) are denoted by n1(e | G) and n2(e | G) , respectively. The Szeged index of the graph G is defined as Sz(G) ( ) ( ) 1 2 n e G n e G e E    . In this paper we compute th...

Abstract. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also le...

let e be an edge of a g connecting the vertices u and v. define two sets n1 (e | g) andn2(e |g) as n1(e | g)= {xv(g) d(x,u) d(x,v)} and n2(e | g)= {xv(g) d(x,v) d(x,u) }.thenumber of elements of n1(e | g) and n2(e | g) are denoted by n1(e | g) and n2(e | g) ,respectively. the szeged index of the graph g is defined as sz(g) ( ) ( ) 1 2 n e g n e g e e    . inthis paper we compute the sz...

Let G be a graph. The first Zagreb polynomial M1(G, x) and the third Zagreb polynomial M3(G, x) of the graph G are defined as:     ( ) ( , ) [ ] e uv E G G x x d(u) + d(v) M1 , ( , )  euvE(G) G x x|d(u) - d(v)| M3 . In this paper, we compute the first and third Zagreb polynomials of Cartesian product of two graphs and a type of dendrimers.

The adaptive responses of crop genotypes and patterns of genotype x location (G x L) interaction are important to crop improvement as they are the basis for selection for specific adaptation and for elucidation of the causes of G x L interaction. Their legitimate assessment, however, requires yield data for the test genotypes for a large number of sites and over multiple years. Such data are se...

The edge tenacity Te(G) of a graph G is dened as:Te(G) = min {[|X|+τ(G-X)]/[ω(G-X)-1]|X ⊆ E(G) and ω(G-X) > 1} where the minimum is taken over every edge-cutset X that separates G into ω(G - X) components, and by τ(G - X) we denote the order of a largest component of G. The objective of this paper is to determine this quantity for split graphs. Let G = (Z; I; E) be a noncomplete connected split...

the edge tenacity te(g) of a graph g is dened as:te(g) = min {[|x|+τ(g-x)]/[ω(g-x)-1]|x ⊆ e(g) and ω(g-x) > 1} where the minimum is taken over every edge-cutset x that separates g into ω(g - x) components, and by τ(g - x) we denote the order of a largest component of g. the objective of this paper is to determine this quantity for split graphs. let g = (z; i; e) be a noncomplete connected spli...

Several association studies support the hypothesis that genetic variants can modify the influence of environmental factors on behavioral outcomes, i.e., G x E interaction. The case-control design used in these studies is powerful, but population stratification with respect to allele frequencies can give rise to false positive or false negative associations. Stratification with respect to the en...