We give a decomposition formula of the zeta function of a regular covering of a graph G with respect to equivalence classes of prime, reduced cycles of G. Furthermore, we give a decomposition formula of the zeta function of a g-cyclic -cover of a symmetric digraph D with respect to equivalence classes of prime cycles of D, for any 0nite group and g∈ . c © 2002 Elsevier Science B.V. All rights r...

The development of computational techniques for the vertex partitioning of graphs and for the machine generation of automorphism groups has received considerable attention in recent years.'-I4 The related problems pertinent to the molecular structure seek to generate nuclear partitioning under the three-dimensional molecular symmetry. In fact, it is envisaged that faster algorithms for the mach...

A graph dynamical system consists of an undirected graph Y where each vertex is assigned a state from a finite set K, an update function for each vertex that depends only on the state of the vertex and its neighbors, and a method that dictates how to compose these functions. A common subclass of graph dynamical systems are sequential dynamical systems, or SDSs, where the update functions are ap...

We introduce two new techniques to the analysis on fractals. One is based on the presentation of the fractal as the boundary of a countable Gromov hyperbolic graph, whereas the other one consists in taking all possible “backward” extensions of the above hyperbolic graph and considering them as the classes of a discrete equivalence relation on an appropriate compact space. Illustrating these tec...

We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva in [CDPR12] between the set of rectangular standard Young tableaux and the set of equivalence classes of chip configurations on certain metric graphs under the relation of linear equivalence. We present an explicit formula for computing the v0-reduced divisors (representatives of the equivalence classes) associated to...

We introduce two new techniques to the analysis on fractals. One is based on the presentation of the fractal as the boundary of a countable Gromov hyperbolic graph, whereas the other one consists in taking all possible \backward" extensions of the above hyperbolic graph and considering them as the classes of a discrete equivalence relation on an appropriate compact space. Illustrating these tec...

a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...