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The contraction of a pair of vertices v_i and v_j of a graph, also called vertex identification, is the operation that produces a graph in which the two nodes v_1 and v_2 are ...

The Floyd-Warshall algorithm, also variously known as Floyd's algorithm, the Roy-Floyd algorithm, the Roy-Warshall algorithm, or the WFI algorithm, is an algorithm for ...

The maximum flow between vertices v_i and v_j in a graph G is exactly the weight of the smallest set of edges to disconnect G with v_i and v_j in different components (Ford ...

A maximum irredundant set is an irredundant set of largest possible size in a graph. Note that a maximum irredundant set is not equivalent to a maximal irredundant set, which ...

The minimum leaf number ml(G) of a connected graph G is the smallest number of tree leaves in any of its spanning trees. (The corresponding largest number of leaves is known ...

The detour matrix Delta, sometimes also called the maximum path matrix or maximal topological distances matrix, of a graph is a symmetric matrix whose (i,j)th entry is the ...

Guy's conjecture, which has not yet been proven or disproven, states that the graph crossing number for a complete graph K_n is ...

The first Zagreb index for a graph with vertex count n and vertex degrees d_i for i=1, ..., n is defined by Z_1=sum_(i=1)^nd_i^2. The notations Z_1 (e.g., Lin et al. 2023) ...

A graph G is transitive if any three vertices (x,y,z) such that edges (x,y),(y,z) in G imply (x,z) in G. Unlabeled transitive digraphs are called digraph topologies.

The lower matching number of a graph is the minimum size of a maximal independent edge set. The (upper) matching number may be similarly defined as the largest size of an ...