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A connected graph G is said to be t-tough if, for every integer k>1, G cannot be split into k different connected components by the removal of fewer than tk vertices. The ...

Das (2018) defines the triameter of a connected graph G with vertex set V and vertex count at least 3 as tr(G)=max{d(u,v)+d(v,w)+d(u,w):u,v,w in V}, where d(i,j) is the graph ...

Assignment of each graph edge of a graph to one of two color classes (commonly designation "red" and "green").

The union G=G_1 union G_2 of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph with V=V_1 union V_2 and X=X_1 union X_2 (Harary ...

"Vertex" is a synonym for a node of a graph, i.e., one of the points on which the graph is defined and which may be connected by graph edges. The terms "point," "junction," ...

Suppose that G is a pseudograph, E is the edge set of G, and C is the family of edge sets of graph cycles of G. Then C obeys the axioms for the circuits of a matroid, and ...

A graphic sequence is a sequence of numbers which can be the degree sequence of some graph. A sequence can be checked to determine if it is graphic using GraphicQ[g] in the ...

A partition {a_1,...,a_n} is called graphical if there exists a graph G having degree sequence {a_1,...,a_n}. The number of graphical partitions of length n is equal to the ...

A graphoid consists of a set M of elements together with two collections C and D of nonempty subsets of M, called circuits and cocircuits respectively, such that 1. For any C ...

An (m+1)-dimensional subspace W of an (n+1)-dimensional vector space V can be specified by an (m+1)×(n+1) matrix whose rows are the coordinates of a basis of W. The set of ...