A signed graph (G,σ) on n vertices is called a parity if there bijection f:V(G)→{1,2,…,n} such that for each edge e=uv of G, f(u) and f(v) have the same σ(e)=1, opposite parities σ(e)=−1. The signature σ parity-signature G. Let Σ−(G) denote set number negative edges over all possible parity-signatures σ. rna σ−(G) G given by σ−(G)=minΣ−(G). In other words, minimum cardinality an edge-cut in two...

let a be a banach algebra and x be a banach a-bimodule. in this paper, we dene a new product on a  x and generalize the module extension banach algebras. we obtain characterizations of arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new banach algebra.

in the present study, the cooperative and diminutive interplay between halogen, hydride, and cation-σ interactions are studied in hmgh···li+(na+)···nccl, li+(na+)···hmgh···clcn and hmgh···clcn···li+(na+) complexes by means of ab initio calculations. to better understand the cooperative or diminutive effects in the ternary systems, the corresponding binary complexes are also considered. the esti...

A quadrangular embedding of a graph in surface Σ, also known as quadrangulation is cellular which every face bounded by 4-cycle. Σ minimal if there no (simple) smaller order Σ. In this paper we determine n(Σ), the for all surfaces, both orientable and nonorientable. Letting S0 denote sphere N2 Klein bottle, prove that n(S0)=4,n(N2)=6, n(Σ)=⌈(5+25−16χ(Σ))/2⌉ other surfaces where χ(Σ) Euler chara...