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A chordless cycle of a graph G is a graph cycle in G that has no cycle chord. Unfortunately, there are conflicting conventions on whether or not 3-cycles should be considered ...

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 ...

The Paulus graphs are the 15 strongly regular graphs on 25 nodes with parameters (nu,k,lambda,mu)=(25,12,5,6) and the 10 strongly regular graphs on 26 nodes with parameters ...

The quadratic embedding constant QEC(G) of a finite simple connected graph G on n vertices is defined as the maximum of the product vDv over all real n-vectors v satisfying ...

The kurtosis excess of a distribution is sometimes called the excess, or excess coefficient. In graph theory, excess refers to the quantity e=n-n_l(v,g) (1) for a v-regular ...

The ratio of the independence number of a graph G to its vertex count is known as the independence ratio of G (Bollobás 1981). The product of the chromatic number and ...

The Krackhardt kite is the simple graph on 10 nodes and 18 edges illustrated above. It arises in social network theory. It is implemented in the Wolfram Language as ...

There are at least two graphs associated with H. Walther. A graph on 25 vertices which appears somewhat similar to Tutte's fragment is implemented without discussion or ...

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. ...

The total domination number gamma_t of a graph is the size of a smallest total dominating set, where a total dominating set is a set of vertices of the graph such that all ...