the inflation $g_{i}$ of a graph $g$ with $n(g)$ vertices and $m(g)$ edges is obtained from $g$ by replacing every vertex of degree $d$ of $g$ by a clique, which is isomorph to the complete graph $k_{d}$, and each edge $(x_{i},x_{j})$ of $g$ is replaced by an edge $(u,v)$ in such a way that $uin x_{i}$, $vin x_{j}$, and two different edges of $g$ are replaced by non-adjacent edges of $g_{i}$. t...

for an arbitrary ring $r$, the zero-divisor graph of $r$, denoted by $gamma (r)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $r$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. it is well-known that for any commutative ring $r$, $gamma (r) cong gamma (t(r))$ where $t(r)$ is the (total) quotient ring of $r$. in this...

in this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.

Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$.  Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the pa...

Often multidimensional data are visualized by splitting n-D data to a set of low dimensional data. While it is useful it destroys integrity of n-D data, and leads to a shallow understanding complex n-D data. To mitigate this challenge a difficult perceptual task of assembling low-dimensional visualized pieces to the whole n-D vectors must be solved. Another way is a lossy dimension reduction by...

The convergence analysis of the power flow methodologies for direct current (dc) electrical networks is addressed in this paper. Banach fixed-point theorem employed to prove and uniqueness solution two different alternatives based on graph theory named successive approximations triangular-based flow. approximation method works with radial mesh grids, including multiple voltage-controlled source...

Circles are frequently used for modelling the growth of particle aggregates through the Voronoi diagram of circles, that is a special instance of the Johnson-Mehl tessellation. The Voronoi diagram of a set of sites is a decomposition of space into proximal regions. The proximal region of a site is the locus of points closer to that site than to any other one. Voronoi diagrams allow one to answe...

in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

The Gallai graph and the anti-Gallai graph of a graph G are edge disjoint spanning subgraphs of the line graph L(G). The vertices in the Gallai graph are adjacent if two of the end vertices of the corresponding edges in G coincide and the other two end vertices are nonadjacent in G. The anti-Gallai graph of G is the complement of its Gallai graph in L(G). Attributed to Gallai (1967), the study ...