This article reviews and discusses a geometric perspective on the well-known fact in graph theory that effective resistance is metric nodes of graph. The classical proofs this make use ideas from electrical circuits or random walks; here we describe an alternative approach which combines (using simplices) algebraic Schur complement) ideas. These perspectives are unified matrix identity Miroslav...

s 6 Awad H. Al-Mohy An Improved Algorithm for the Matrix Logarithm . . . . . . . . . . . . . . . . . . . . 7 David Amsallem Interpolation on Matrix Manifolds of Reduced-Order Models and Application to On-Line Aeroelastic Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Athanasios C. Antoulas Model Reduction of Parameter-Dependent Systems . . . . . . . . . . . . . . . . . . ...

A concept related to the spectrum of a graph is that of energy. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G . The Laplacian energy of a graph G is equal to the sum of distances of the Laplacian eigenvalues of G and the average degree d(G) of G. In this paper we introduce the concept of Laplacian energy of fuzzy graphs. ...

Model checking is an automatic technique for software verification through which all reachable states are generated from an initial state to finding errors and desirable patterns. In the model checking approach, the behavior and structure of system should be modeled. Graph transformation system is a graphical formal modeling language to specify and model the system. However, modeling of large s...

it is necessary to generate the automorphism group of a chemical graph in computer-aidedstructure elucidation. an euclidean graph associated with a molecule is defined by a weightedgraph with adjacency matrix m = [dij], where for i≠j, dij is the euclidean distance between thenuclei i and j. in this matrix dii can be taken as zero if all the nuclei are equivalent. otherwise,one may introduce dif...

‎let $g$ be a graph with vertex set $v(g)$ and edge set $x(g)$ and consider the set $a={0,1}$‎. ‎a mapping $l:v(g)longrightarrow a$ is called binary vertex labeling of $g$ and $l(v)$ is called the label of the vertex $v$ under $l$‎. ‎in this paper we introduce a new kind of graph energy for the binary labeled graph‎, ‎the labeled graph energy $e_{l}(g)$‎. ‎it depends on the underlying graph $g$...

Several well-known results from the random matrix theory, such as Wigner’s law and the Marchenko–Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the limiting spectral measure play a rôle in this approach.

We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the Wiener maximum quadratic assignment problem, is NP-hard in the ordinary sense and solvable in pseudo-polynomial time. Our approach also yields a polynomial time...