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The algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph G. In other ...

Given n points, find the line segments with the shortest possible total length which connect the points. The segments need not necessarily be straight from one point to ...

The distance polynomial is the characteristic polynomial of the graph distance matrix. The following table summarizes distance polynomials for some common classes of graphs. ...

A generalized dodecagon is a generalized polygon of order 12. GD(1,2) is the (3,12)-cage graph, more commonly known as the Tutte 12-cage. GD(2,1) is the line graph of the ...

The rank polynomial R(x,y) of a general graph G is the function defined by R(x,y)=sum_(S subset= E(G))x^(r(S))y^(s(S)), (1) where the sum is taken over all subgraphs (i.e., ...

A minimum vertex cut of a graph is a vertex cut of smallest possible size. A vertex cut set of size 1 in a connected graph corresponds to an articulation vertex. The size of ...

An edge cut (Holton and Sheehan 1993, p. 14; West 2000, p. 152), edge cut set, edge cutset (Holton and Sheehan 1993, p. 14), or sometimes simply "cut set" or "cutset" (e.g., ...

The circuit rank gamma, also denoted mu (Volkmann 1996, Babić et al. 2002) or beta (White 2001, p. 56) and known as the cycle rank (e.g., White 2001, p. 56), (first) graph ...

A Möbius ladder, sometimes called a Möbius wheel (Jakobson and Rivin 1999), of order n is a simple graph obtained by introducing a twist in a prism graph of order n that is ...

A minimum edge cut of a graph is an edge cut of smallest possible size. The size of a minimum edge cut in a connected graph G is called the graph's edge connectivity ...