In this paper the properties of node-node adjacency matrix in acyclic digraphs are considered. It is shown that topological ordering and node-node adjacency matrix are closely related. In fact, first the one to one correspondence between upper triangularity of node-node adjacency matrix and existence of directed cycles in digraphs is proved and then with this correspondence other properties of ...

Stress is a centrality measure determined by the shortest paths passing through given vertex. Noting that adjacency matrix playing an important role in finding distance and number of between pair vertices, interesting expression also algorithm are presented to find stress using matrix. The results suitably adopted obtain betweenness measure. Further extended cases Cartesian product G□H graphs, ...

Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N)...

Given a pair of keyframe formations for a group consisting of multiple individuals, we present a spectral-based approach to smoothly transforming a source group formation into a target formation while respecting the clusters of the involved individuals. The proposed method provides an effective means for controlling the macroscopic spatiotemporal arrangement of individuals for applications such...

given a pair (semispray $s$, metric $g$) on a tangent bundle, the family of nonlinear connections $n$ such that $g$ is recurrent with respect to $(s, n)$ with a fixed recurrent factor is determined by using the obata tensors. in particular, we obtain a characterization for a pair $(n, g)$ to be recurrent as well as for the triple $(s, stackrel{c}{n}, g)$ where $stackrel{c}{n}$ is the canonical ...

Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical ...

Characterizing graphs by their spectra is an important topic in spectral graph theory, which has attracted a lot of attention researchers recent years. It generally very hard and challenging to show given determined its spectrum. In Wang (2017), the author gave simple arithmetic condition for family being generalized spectra. However, method applies only so called controllable ; it fails when a...

The weighted Sitting Closer to Friends than Enemies (SCFE) problem is find an injection of the vertex set a given graph into metric space so that, for every pair incident edges with different weight, end vertices heavier edge are closer lighter edge. Seriation simultaneous reordering rows and columns symmetric matrix such that entries monotone nondecreasing in when moving towards diagonal. If e...