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The edge count of a graph g, commonly denoted M(g) or E(g) and sometimes also called the edge number, is the number of edges in g. In other words, it is the cardinality of ...

Let A be an n×n matrix with complex or real elements with eigenvalues lambda_1, ..., lambda_n. Then the spectral radius rho(A) of A is rho(A)=max_(1<=i<=n)|lambda_i|, i.e., ...

An (n,k)-banana tree, as defined by Chen et al. (1997), is a graph obtained by connecting one leaf of each of n copies of an k-star graph with a single root vertex that is ...

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. ...

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 ...

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 ...

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 ...

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 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 ...