a group $g$ is said to be a c-tidy group if for every element $x in g setminus k(g)$‎, ‎the set $cyc(x)=lbrace y in g mid langle x‎, ‎y rangle ; {rm is ; cyclic} rbrace$ is a cyclic subgroup of $g$‎, ‎where $k(g)=underset{x in g}bigcap cyc(x)$‎. ‎in this short note we determine the structure of finite c-tidy groups‎.

Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...

a graph $g$ is called a fractional‎ ‎$(k,n',m)$-critical deleted graph if any $n'$ vertices are removed‎ ‎from $g$ the resulting graph is a fractional $(k,m)$-deleted‎ ‎graph‎. ‎in this paper‎, ‎we prove that for integers $kge 2$‎, ‎$n',mge0$‎, ‎$nge8k+n'+4m-7$‎, ‎and $delta(g)ge k+n'+m$‎, ‎if‎ ‎$$|n_{g}(x)cup n_{g}(y)|gefrac{n+n'}{2}$$‎ ‎for each pair of non-adjac...

A theoretical method for the systematic definition and determination of Cartesian and spherical electromagnetic (onshell) formfactors and multipole moments for particles or composite systems from electromagnetic Breit-frame current distributions is presented. The method presented is free of sign ambiguities and is not based on the underlying analytical substructure of the electromagnetic curren...

let $g$ be a group. the order graph of $g$ is the (undirected)graph $gamma(g)$,those whose vertices are non-trivial subgroups of $g$ and two distinctvertices $h$ and $k$ are adjacent if and only if either$o(h)|o(k)$ or $o(k)|o(h)$. in this paper, we investigate theinterplay between the group-theoretic properties of $g$ and thegraph-theoretic properties of $gamma(g)$. for a finite group$g$, we s...

the wiener index $w(g)$ of a connected graph $g$‎ ‎is defined as $w(g)=sum_{u,vin v(g)}d_g(u,v)$‎ ‎where $d_g(u,v)$ is the distance between the vertices $u$ and $v$ of‎ ‎$g$‎. ‎for $ssubseteq v(g)$‎, ‎the {it steiner distance/} $d(s)$ of‎ ‎the vertices of $s$ is the minimum size of a connected subgraph of‎ ‎$g$ whose vertex set is $s$‎. ‎the {it $k$-th steiner wiener index/}‎ ‎$sw_k(g)$ of $g$ ...

Embedding of Klein-Gordon and Dirac particle onto Riemannian submanifold in higher dimensional Minkowski space is given by using Hamiltonian BRST formalism. Up to the ordering and quantum potential term induced by embedding, obtained K-G equation is the usual one in Riemannian space, instead, the obtained Dirac equation is essentially different from the usual well known form using vierbein. The...

This chapter should be cited as: Cubasch, U., D. Wuebbles, D. Chen, M.C. Facchini, D. Frame, N. Mahowald, and J.-G. Winther, 2013: Introduction. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, ...