Search Results for ""

The edge multiplicity of a given end vertex in a multigraph is the number of multiple edges sharing that end vertex. The maximum edge multiplicity in such a graph is known as ...

Let G be a finite graph and v a vertex of G. The stabilizer of v, stab(v), is the set of group elements {g in Aut(G)|g(v)=v}, where Aut(g) is the graph automorphism group. ...

Given a graph G, the arboricity Upsilon(G) is the minimum number of edge-disjoint acyclic subgraphs (i.e., spanning forests) whose union is G. An acyclic graph therefore has ...

The coboundary polynomial chi^__G(q,t) is a bivariate graph polynomial which can be expressed in terms of the Tutte polynomial T_G(x,y) of a graph G by ...

A block is a maximal connected subgraph of a given graph G that has no articulation vertex (West 2000, p. 155). If a block has more than two vertices, then it is biconnected. ...

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. A vertex coloring that minimize ...

An edge-induced subgraph is a subset of the edges of a graph G together with any vertices that are their endpoints. The subgraph induced by a set of edges can be computed in ...

In a graph G, contraction of an edge e with endpoints u,v is the replacement of u and v with a single vertex such that edges incident to the new vertex are the edges other ...

The chromatic polynomial pi_G(z) of an undirected graph G, also denoted C(G;z) (Biggs 1973, p. 106) and P(G,x) (Godsil and Royle 2001, p. 358), is a polynomial which encodes ...

A minimum edge cover is an edge cover having the smallest possible number of edges for a given graph. The size of a minimum edge cover of a graph is known as the edge cover ...