Mixed almost Moore graphs appear in the context of the Degree/Diameter problem as a class of extremal mixed graphs, in the sense that their order is one less than the Moore bound for mixed graphs. The problem of their existence has been considered before for directed graphs and undirected ones, but not for the mixed case, which is a kind of generalization. In this paper we give some necessary c...

The degree-diameter problem seeks to find the maximum possible order of a graph with a given (maximum) degree and diameter. It is known that graphs attaining the maximum possible value (the Moore bound) are extremely rare, but much activity is focussed on finding new examples of graphs or families of graph with orders approaching the bound as closely as possible. There has been recent interest ...

The zero-divisor graph of a commutative semigroup with zero is the graph whose vertices are the nonzero zero-divisors of the semigroup, with two distinct vertices adjacent if the product of the corresponding elements is zero. New criteria to identify zerodivisor graphs are derived using both graph-theoretic and algebraic methods. We find the lowest bound on the number of edges necessary to guar...

The disk dimension of a planar graph G is the least number k for which G embeds in the plane minus k open disks, with every vertex on the boundary of some disk. Useful properties of graphs with a given disk dimension are derived, leading to an efficient algorithm to obtain an outerplanar subgraph of a graph of disk dimension k by removing at most 2k−2 vertices. This reduction is used to obtain ...

A Gelfand model for an algebra is a module given by direct sum of irreducible submodules, with every isomorphism class modules represented exactly once. We introduce the notion perfect finite Coxeter group, which certain set discrete data (involving Rains and Vazirani's concept involution) that parametrizes associated Iwahori-Hecke algebra. describe models all classical Weyl groups, excluding t...

Term graphs, in which the nodes correspond to distinct lexical units (words or phrases) and the weighted edges represent semantic relatedness between those units, have been previously shown to be beneficial for ad-hoc IR. In this paper, we experimentally demonstrate that indiscriminate utilization of term graphs for query expansion limits their retrieval effectiveness. To address this deficienc...

The paper is devoted to the implementations of the public key algorithms based on simple algebraic graphs A(n, K ) and D(n, K ) defined over the same finite commutative ring K . If K is a finite field both families are families of graphs with large cycle indicator. In fact, the family D(n, Fq) is a family of graphs of large girth (f.g.l.g.) with c = 1, their connected components C D(n, Fq) form...

A graph with unique path property (UPP) has 211 vertices and a unique path of length n between each two vertices. These graphs are very important in the design of architectures and algorithms for interconnection netwp.rks. Given two UPP graphs we introduce an algorithm to determine 'isomorphisrp. betwe,en the graphs. We give two different cpnstructions 2"+1-311-2 for nonisdmorphic UPP graphs'an...

We present an experimental evaluation of an approximate distance oracle recently suggested by Thorup [1] for undirected planar graphs. The oracle uses the existence of graph separators for planar graphs, discovered by Lipton and Tarjan [2], in order to divide the graph into smaller subgraphs. For a planar graph with n nodes, the algorithmic variant considered uses O(n(log n)/ ) preprocessing ti...

In this paper, we propose a new algorithm for error-correcting subgraph isomorphism detection from a set of model graphs to an unknown input graph. The algorithm is based on a compact representation of the model graphs. This representation is derived from the set of model graphs in an off-line preprocessing step. The main advantage of the proposed representation is that common subgraphs of diff...