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The score sequence of a tournament is a monotonic nondecreasing sequence of the outdegrees of the graph vertices of the corresponding tournament graph. Elements of a score ...

Let alpha(G) denote the independence number of a graph G. Then the Shannon capacity Theta(G), sometimes also denoted c(G), of G is defined as ...

A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple ...

Find the minimum size square capable of bounding n equal squares arranged in any configuration. The first few cases are illustrated above (Friedman). The only packings which ...

There are several different definitions of the barbell graph. Most commonly and in this work, the n-barbell graph is the simple graph obtained by connecting two copies of a ...

The cube-connected cycle graph of order n is the graph obtained by replacing each vertex in a n-dimensional hypercube by a cycle of length n. They were introduced by ...

The thickness (or depth) t(G) (Skiena 1990, p. 251; Beineke 1997) or theta(G) (Harary 1994, p. 120) of a graph G is the minimum number of planar edge-induced subgraphs P_i of ...

The Kirchhoff sum index KfS is a graph index defined for a graph on n nodes by KfS=1/2sum_(i=1)^nsum_(j=1)^n((Omega)_(ij))/((d)_(ij)), where (Omega)_(ij) is the resistance ...

Assume that n numbered pancakes are stacked, and that a spatula can be used to reverse the order of the top k pancakes for 2<=k<=n. Then the pancake sorting problem asks how ...

The stability index Z^_(G) of a graph G is defined by Z^_=sum_(k=0)^(|_n/2_|)|c_(2k)|, where c_k is the kth coefficient of the characteristic polynomial and |_n_| denotes the ...