Global Analysis and Discrete Mathematics
http://gadm.du.ac.ir/
Global Analysis and Discrete Mathematicsendaily1Mon, 01 Jun 2020 00:00:00 +0430Mon, 01 Jun 2020 00:00:00 +0430Some Edge Cut Sets and an Upper bound for Edge Tenacity of Organic Compounds CnH2n+2
http://gadm.du.ac.ir/article_163.html
The graphs play an important role in our daily life. For example, the urban transport network can be represented by a graph, as the intersections are the vertices and the streets are the edges of the graph. Suppose that some edges of the graph are removed, the question arises, how damaged the graph is. There are some criteria for measuring the vulnerability of graph; the tenacity is the best criteria for measuring it. In this paper, we nd some edge cut sets for organic compounds CnH2n+2 and obtain an upper bound for Te(CnH2n+2) by these edge cut sets.A note on essentially left $\phi$-contractible Banach algebras
http://gadm.du.ac.ir/article_164.html
In this note, we show that \cite[Corollary 3.2]{sad} is not always true. In fact, we characterize essential left $\phi$-contractibility of the group algebras in terms of compactness of its related locally compact group. Also, we show that for any compact commutative group $G$, $L^{2}(G)$ is always essentially left $\phi$-contractible. We discuss the essential left $\phi$-contractibility of some Fourier algebras.Vertex-Cut Sets and Tenacity of Organic Compounds CnH2n+2
http://gadm.du.ac.ir/article_165.html
Abstract Consider some vertices of a graph G are omitted, there are some ceriteria for measuring the vulnerability of the graph; Tenacity is one of them. In the denition of tenacity we use vertex cut S and some items, (GS) and !(GS), such that (GS) is the number of vertices in the largest compnent of G S and !(G S) is the number of components of G S. In this paper we work on tenacity of organic compound CnH2n+2. The graph of this molecoule is a tree. We try on tenacity of it by the denition of the tenacity.Regularity of Bounded Tri-Linear Maps and the Fourth Adjoint of a Tri-Derivation
http://gadm.du.ac.ir/article_166.html
In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X &times; Y &times; Z &minus;&rarr; W is a bounded tri-linear mapping and h : W &minus;&rarr; S is a bounded linear mapping, then f is regular if and only if hof is regular. We also shall give some necessary and suﬃcient conditions such that the fourth adjoint D^&lowast;&lowast;&lowast;&lowast; of a tri-derivation D is again tri-derivation.A practical algorithm for [r, s, t]-coloring of graph
http://gadm.du.ac.ir/article_167.html
Coloring graphs is one of important and frequently used topics in diverse sciences. In the majority of the articles, it is intended to find a proper bound for vertex coloring, edge coloring or total coloring in the graph. Although it is important to find a proper algorithm for graph coloring, it is hard and time-consuming too. In this paper, a new algorithm for vertex coloring, edge coloring and [r, s, t]- coloring is presented. Then, this algorithm is used to solve the applied problems of eight-queens and [r, s, t]- coloring. Here, there are numerical examples to study the efficiency of the method and to compare the results.