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The mean distance of a (connected) graph is the mean of the elements of its graph distance matrix. Closed forms for some classes of named graphs are given in the following ...

The clique polynomial C_G(x) for the graph G is defined as the polynomial C_G(x)=1+sum_(k=1)^(omega(G))c_kx^k, (1) where omega(G) is the clique number of G, the coefficient ...

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

The detour polynomial of a graph G is the characteristic polynomial of the detour matrix of G. Precomputed detour polynomials for many named graphs are available in the ...

A labeling phi of (the vertices) of a graph G with positive integers taken from the set {1,2,...,r} is said to be r-distinguishing if no graph automorphism of G preserves all ...

A spanning tree of a graph on n vertices is a subset of n-1 edges that form a tree (Skiena 1990, p. 227). For example, the spanning trees of the cycle graph C_4, diamond ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node ...

The Wiener index W, denoted w (Wiener 1947) and also known as the "path number" or Wiener number (Plavšić et al. 1993), is a graph index defined for a graph on n nodes by ...

The Harary index of a graph G on n vertices was defined by Plavšić et al. (1993) as H(G)=1/2sum_(i=1)^nsum_(j=1)^n(RD)_(ij), (1) where (RD)_(ij)={D_(ij)^(-1) if i!=j; 0 if ...