let g be a simple graph with vertex set v(g) {v1,v2 ,...vn} . for every vertex i v , ( ) i  vrepresents the degree of vertex i v . the h-th order of randić index, h r is defined as the sumof terms1 2 11( ), ( )... ( ) i i ih  v  v  vover all paths of length h contained (as sub graphs) in g . inthis paper , some bounds for higher randić index and a method for computing the higherrandic ind...

‎‎for a finite group $g$ and a subgroup $h$ of $g$‎, ‎the relative commutativity degree of $h$ in $g$‎, ‎denoted by $d(h,g)$‎, ‎is the probability that an element of $h$ commutes with an element of $g$‎. ‎let $mathcal{d}(g)={d(h,g):hleq g}$ be the set of all relative commutativity degrees of subgroups of $g$‎. ‎it is shown that a finite group $g$ admits three relative commutativity degrees if a...

We draw upon diverse datasets to compare the institutional organizational of upstream life science research across the United States and Europe. Understanding cross-national differences in the organization of innovative labor in the life sciences requires attention to the structure and evolution of biomedical networks involving public research organizations (universities, government laboratorie...

The existence of specialized scales in adult male Lepidoptera has long been recognized, and they were first named androconia by Scudder (1877). Müller (1877a) believed that such structures had evolved as a result of sexual selection and that they were involved in the dissemination of scents or pheromones to influence female behaviour, a theory that has now been proven by experiments on the cour...

Adviser: Professor Mark Brittenham We study Richard Thompson's group V , and some generalizations of this group. V was one of the first two examples of a finitely presented, infinite, simple group. Since being discovered in 1965, V has appeared in a wide range of mathematical subjects. Despite many years of study, much of the structure of V remains unclear. Part of the difficulty is that the st...

We consider the notion of replete object in the category of directed complete partial orders and Scott-continuous functions, and show that, contrary to previous expectations, there are non-replete objects. The same happens in the case of ω-complete posets. Synthetic Domain Theory developed from an idea of Dana Scott: it is consistent with intuitionistic set theory that all functions between dom...

The Scott rank of a countable structure is a measure, coming from the proof of Scott’s isomorphism theorem, of the complexity of that structure. The Scott spectrum of a theory (by which we mean a sentence of Lω1ω) is the set of Scott ranks of countable models of that theory. In ZFC + PD we give a descriptive-set-theoretic classification of the sets of ordinals which are the Scott spectrum of a ...

let $a$ be a non-trivial abelian group and $a^{*}=asetminus {0}$. a graph $g$ is said to be $a$-magic graph if there exists a labeling$l:e(g)rightarrow a^{*}$ such that the induced vertex labeling$l^{+}:v(g)rightarrow a$, define by $$l^+(v)=sum_{uvin e(g)} l(uv)$$ is a constant map.the set of all constant integerssuch that $sum_{uin n(v)} l(uv)=c$, for each $vin n(v)$,where $n(v)$ denotes the s...

‎suppose $n$ is a fixed positive integer‎. ‎we introduce the relative n-th non-commuting graph $gamma^{n} _{h,g}$‎, ‎associated to the non-abelian subgroup $h$ of group $g$‎. ‎the vertex set is $gsetminus c^n_{h,g}$ in which $c^n_{h,g} = {xin g‎ : ‎[x,y^{n}]=1 mbox{~and~} [x^{n},y]=1mbox{~for~all~} yin h}$‎. ‎moreover‎, ‎${x,y}$ is an edge if $x$ or $y$ belong to $h$ and $xy^{n}eq y^{n}x$ or $x...

Let G be a finite group and C(G) be the family of representative conjugacy classes of‎ ‎subgroups of G‎. ‎The matrix whose H,K-entry is the number of ‎fixed points of the set G/K under the action of H is called the‎ ‎table of marks of G where H,K run through all elements in‎ C(G)‎. Shinsaku Fujita for the first time introduced the term “markaracter” to discuss marks for permutation representati...