let $d$ be a digraph with skew-adjacency matrix $s(d)$‎. ‎the skew‎ ‎energy of $d$ is defined as the sum of the norms of all‎ ‎eigenvalues of $s(d)$‎. ‎two digraphs are said to be skew‎ ‎equienergetic if their skew energies are equal‎. ‎we establish an‎ ‎expression for the characteristic polynomial of the skew‎ ‎adjacency matrix of the join of two digraphs‎, ‎and for the‎ ‎respective skew energ...

One of the basic concerns of Geographic Information Systems and their application is the spatial relationships between objects on the map. This has been attacked from two directions: by the construction/linking of polygon boundary segments; and by including spatial operators within data-base retrieval requests. In both cases only an incomplete picture has been obtained due to the lack of any co...

We consider the problem of computing all-pairs shortest paths in a directed graph with real weights assigned to vertices. For an n × n 0 − 1 matrix C, let KC be the complete weighted graph on the rows of C where the weight of an edge between two rows is equal to their Hamming distance. Let MWT (C) be the weight of a minimum weight spanning tree of KC . We show that the all-pairs shortest path p...

We analyse a huge and very precise trace of contact data collected during 6 months on the entire population of a rehabilitation hospital. We investigate the graph structure of the average daily contact network. Our main results are to unveil striking properties of this structure in the considered hospital, and to present a methodology that can be used for analysing any dynamic complex network w...

A lower bound on the chromatic number of a graph is derived by majorization of spectra of weighted adjacency matrices. These matrices are given by Hadamard products of the adjacency matrix and arbitrary Hermitian matrices.

In this note, we give some examples of links having 2-adjacency relation and we also report a recent study of 2-bridge links with 2-adjacency relation by the author.

We give a necessary and su cient condition for a graphical regu lar representation to be adjacency transitive and provide an in nite family of nite simple undirected vertex transitive graphs such that neither nor c is adjacency transitive

The problem of placing resources in a k-ary n-cube (k > 2) is considered in this paper. For a given j 1, resources are placed such that each non-resource node is adjacent to j resource nodes. We rst prove that perfect j-adjacency placements are impossible in k-ary n-cubes if n < j < 2n. Then, we show that a perfect j-adjacency placement is possible in k-ary n-cubes when one of the following two...

The word "place" is curiously wide in its application, going beyond strict spatiality. A traditional town is a place, the right half of that field is a place, the vacuum cleaner has its place in the closet, the children's place is upstairs, the woman's place was in the home, the third line on the form is the place for this year's income, and as we grow up we try to find our place within the mes...

Proof. We first recall that every non-singular matrix B can be written B = QR, where Q is an orthonormal matrix Q and R is upper-triangular matrix R with positive diagonals1 We will use a slight variation of this fact, writing B = RQ. Now, since QT = Q−1, QAQT has exactly the same eigenvalues as A. Let Rt be the matrix t ∗R+ (1− t)I, and consider the family of matrices Mt = RtQAQR t , as t goes...