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The maximum number of disjoint dominating sets in a domatic partition of a graph G is called its domatic number d(G). The domatic number should not be confused with the ...

Let I(x,y) denote the set of all vertices lying on an (x,y)-graph geodesic in G, then a set S with I(S)=V(G) is called a geodetic set in G and is denoted g(G).

The co-rank of a graph G is defined as s(G)=m-n+c, where m is the number of edges of G, n is the number of vertices, and c is the number of connected components (Biggs 1993, ...

The rank of a graph G is defined as r(G)=n-c, where n is the number of vertices on G and c is the number of connected components (Biggs 1993, p. 25).

A connection between two or more vertices of a hypergraph. A hyperedge connecting just two vertices is simply a usual graph edge.

A maximum clique of a graph G is a clique (i.e., complete subgraph) of maximum possible size for G. Note that some authors refer to maximum cliques simply as "cliques." The ...

The maximum degree, sometimes simply called the maximum degree, of a graph G is the largest vertex degree of G, denoted Delta.

The mean clustering coefficient of a graph G is the average of the local clustering coefficients of G. It is implemented in the Wolfram Language as ...

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. A vertex coloring that minimize ...

A minimum vertex cover is a vertex cover having the smallest possible number of vertices for a given graph. The size of a minimum vertex cover of a graph G is known as the ...