This paper presents a solution of the polycirculant conjecture which states that every vertex-transitive graph G has an automorphism that permutes the vertices in cycles of the same length. This is done by identifying vertex-transitive graphs as coset graphs. For a coset graph H, an equivalence relation ∼ is defined on the vertices of cosets with classes as double cosets of the stabiliser and a...

We give a hypergraph rewriting semantics for the polyadic π-calculus, based on rewriting rules equivalent to those in the double-pushout approach. The structural congruence of the π-calculus is replaced by hypergraph isomorphism. The correctness of the encoding from the graph-based notation into π-calculus can be shown by using an intermediate notation, so-called name-based graph terms.

We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B3(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D4(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite double of the former.

We shall prove that a connected graph G is projective-planar if and only if it has a 2n-fold planar connected covering obtained as a composition of an n-fold covering and a double covering for some n¿ 1 and show that every planar regular covering of a nonplanar graph is such a composite covering. c © 2002 Elsevier Science B.V. All rights reserved.

Consider the following problem: Given a complete geometric graph, how many plane spanning trees can be packed into its edge set? We investigate this question for plane spanning double stars instead of general spanning trees. We give a necessary, as well as a sufficient condition for the existence of packings with a given number of plane spanning double stars. We also construct complete geometri...

This paper deals with the double integrator consensus problem. The objective is the design of a new consensus algorithm for continuous-time multi-agent systems. The dynamic of agents is assumed to be of double integrator type. The proposed algorithm considers that there are no sensors to measure the velocity of the agents. Thus the classical double integrator consensus algorithm leads to an osc...

A μ-simultaneous edge coloring of graph G is a set of μ proper edge colorings of G with a same color set such that for each vertex, the sets of colors appearing on the edges incident to that vertex are the same in each coloring and no edge receives the same color in any two colorings. The μ-simultaneous edge coloring of bipartite graphs has a close relation with μ-way Latin trades. Mahdian et a...

We introduce weak oddness ωw, a new measure of uncolourability of cubic graphs, defined as the least number of odd components in an even factor. For every bridgeless cubic graph G, %(G) ≤ ωw(G) ≤ ω(G), where %(G) denotes the resistance of G and ω(G) denotes the oddness of G, so this new measure is an approximation of both oddness and resistance. We demonstrate that there are graphs G satisfying...

It belongs to the folklore that graph grammars can be seen as a proper generalisation of Petri nets. In this paper we show how this intuitive relationship can be made formal. The double-pushout approach to graph rewriting turns out to be strictly related to Petri nets with read and inhibitor arcs, while the single-pushout approach has strong connections to Petri nets with read and reset arcs.

Let H be a cubic graph admitting a 3-edge-coloring c : E(H) → Z3 such that the edges colored with 0 and μ ∈ {1, 2} induce a Hamilton circuit of H and the edges colored with 1 and 2 induce a 2-factor F . The graph H is semi-Kotzig if switching colors of edges in any even subgraph of F yields a new 3-edge-coloring ofH having the same property as c . A spanning subgraphH of a cubic graph G is call...