This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that it lacks the formality and rigour of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that standard string edit distance techniques can be used. To do this we use graph spectral seri...

Algebraic combinatorics is the area of mathematics that uses the theories and methods of abstract and linear algebra to solve combinatorial problems, or conversely applies combinatorial techniques to solve problems in algebra. In particular, spectral graph theory applies the techniques of linear algebra to study graph theory. Spectral graph theory is the study of the eigenvalues of various matr...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

Yu. Dabaghian Department of Physiology, Keck Center for Integrative Neuroscience, University of California, San Francisco, California 94143-0444, USA e-mail [email protected] (August 15, 2006) A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obt...

Let (Gε)ε>0 be a family of ’ε-thin’ Riemannian manifolds modeled on a finite metric graph G, for example, the ε-neighborhood of an embedding of G in some Euclidean space with straight edges. We study the asymptotic behavior of the spectrum of the Laplace-Beltrami operator on Gε as ε → 0, for various boundary conditions. We obtain complete asymptotic expansions for the kth eigenvalue and the eig...

Sensor coverage will benefit from finding better ways to communicate among smaller sensors. Also, as development in nanotechnology progresses, the need for low-cost, robust, reliable communication among nano-machines will become apparent. Communication and signaling within newly engineered inorganic and biological nano-systems will allow for extremely dense and efficient distributed operation. ...

Given a graph G with vertex set V (G) = V and edge set E(G) = E, let Gl be the line graph and Gc the complement of G. Let G0 be the graph with V (G0) = V and with no edges, G1 the complete graph with the vertex set V , G+ = G and G− = Gc. Let B(G) (Bc(G)) be the graph with the vertex set V ∪E and such that (v, e) is an edge in B(G) (resp., in Bc(G)) if and only if v ∈ V , e ∈ E and vertex v is ...