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The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...

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 Wiener sum index WS is a graph index defined for a graph on n nodes by WS=1/2sum_(i=1)^nsum_(j=1)^n((d)_(ij))/((Omega)_(ij)), where (d)_(ij) is the graph distance matrix ...

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

A complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with n graph vertices is denoted K_n and has (n; 2)=n(n-1)/2 (the ...

The cubical graph is the Platonic graph corresponding to the connectivity of the cube. It is isomorphic to the generalized Petersen graph GP(4,1), bipartite Kneser graph ...

A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i ...

The dodecahedral graph is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings. The left embedding ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...