‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...

We propose an algorithmic framework for convex minimization problems of composite functions with two terms: a self-concordant part and a possibly nonsmooth regularization part. Our method is a new proximal Newton algorithm with local quadratic convergence rate. As a specific problem instance, we consider sparse precision matrix estimation problems in graph learning. Via a careful dual formulati...

the order graph of a group $g$, denoted by $gamma^*(g)$, is a graph whose vertices are subgroups of $g$ and two distinct vertices $h$ and $k$ are adjacent if and only if $|h|big{|}|k|$ or $|k|big{|}|h|$. in this paper, we study the connectivity and diameter of this  graph. also we give a relation between the order graph and prime  graph of a group.

let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...

in this paper, we first collect the earlier results about some graph operations and then wepresent applications of these results in working with chemical graphs.

Model-driven development (MDD) has become a promising trend in software engineering. The model-driven development of highly complex software systems may lead to large models which deserve a modularization concept to enable their structured development in larger teams. Graphs are a natural way to represent the underlying structure of visual models. Typed graphs with inheritance and containment a...

A new method is proposed to measure software system security. Each component can be characterized by a composite net which combines the features of Finite State Machine and Operation Diagram. A fuzzy number is introduced to this net to represent uncertain elements that might affect the software security, and thus we construct Security Function for each component. The whole system Security Index...

Let G be a connected graph. The multiplicative Zagreb eccentricity indices of G are defined respectively as Π1(G) = ∏ v∈V (G) ε 2 G(v) and Π ∗ 2(G) = ∏ uv∈E(G) εG(u)εG(v), where εG(v) is the eccentricity of vertex v in graph G and εG(v) = (εG(v)) . In this paper, we present some bounds of the multiplicative Zagreb eccentricity indices of Cartesian product graphs by means of some invariants of t...

An overall goal of the INCOSE MBSE initiative is to provide SysML with a formal semantics and to integrate reasoning services as part of system engineering. UML class diagrams have been encoded as Knowledge Bases (KB) within the Description Logic (DL), ALCQI. The encoding provides a formal semantics for class diagrams which accords with the informal semantics. The encoding applies to SysML whic...

A composite hip prosthesis (CHP) made from alumina reinforced ultra high molecular weight polyethylene (UHMWPE) was designed and manufactured. The main objective of the study was to fabricate the composite hip prosthesis which would be an ideal replacement of metallic one as bone is a composite material consisting of collagen fibre matrix and embedded hydroxyapatite mineral. With this idea we d...