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The smallest cubic graphs with graph crossing number CN(G)=n have been termed "crossing number graphs" or n-crossing graphs by Pegg and Exoo (2009). The n-crossing graphs are ...

Let S be a collection of subsets of a finite set X. A subset Y of X that meets every member of S is called the vertex cover, or hitting set. A vertex cover of a graph G can ...

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 theory is decidable iff there is an algorithm which can determine whether or not any sentence r is a member of the theory.

The (lower) domination number gamma(G) of a graph G is the minimum size of a dominating set of vertices in G, i.e., the size of a minimum dominating set. This is equivalent ...

There are at least two results known as "the area principle." The geometric area principle states that (|A_1P|)/(|A_2P|)=(|A_1BC|)/(|A_2BC|). (1) This can also be written in ...

In graph theory, a cycle graph C_n, sometimes simply known as an n-cycle (Pemmaraju and Skiena 2003, p. 248), is a graph on n nodes containing a single cycle through all ...

As proposed by Hosoya (1971), the Hosoya index (also called Z-index) of a graph is defined by Z = sum_(k=0)^(n)|a_k| (1) = sum_(k=0)^(n)b_k, (2) where n is the number of ...

An independent vertex set of a graph G is a subset of the vertices such that no two vertices in the subset represent an edge of G. The figure above shows independent sets ...

The Möbius-Kantor graph is the unique cubic symmetric graph on 16 nodes, illustrated above in several embeddings. Its unique canonical LCF notation is [5,-5]^8. The ...