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Let a simple graph G have n vertices, chromatic polynomial P(x), and chromatic number chi. Then P(G) can be written as P(G)=sum_(i=0)^ha_i·(x)_(p-i), where h=n-chi and (x)_k ...

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 skeleton of the bislit cube is the 8-vertex simple graph, illustrated above in several embeddings, which consists of a cube in which two opposite faces have polyhedron ...

A Hamiltonian walk on a connected graph is a closed walk of minimal length which visits every vertex of a graph (and may visit vertices and edges multiple times). For ...

The disorder number of a simple connected graph on n vertices is defined as the maximum length of a walk along the edges of the graph taken over all ordering of its vertices ...

There are several theorems known as the "sandwich theorem." In calculus, the squeeze theorem is also sometimes known as the sandwich theorem. In graph theory, the sandwich ...

An odd chordless cycle is a chordless cycle of length >4. A graph is said to be perfect iff neither the graph G nor its graph complement G^_ has an odd chordless cycle. A ...

subjMathematics:Discrete Mathematics:Graph Theory:Cliques The maximal clique polynomial C_G(x) for the graph G may be defined as the polynomial ...

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 ...

Let c_k be the number of edge covers of a graph G of size k. Then the edge cover polynomial E_G(x) is defined by E_G(x)=sum_(k=0)^mc_kx^k, (1) where m is the edge count of G ...