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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 ...

A tree not having the complete bipartite graph K_(1,2) with base at the vertex of degree two as a limb (Lu et al. 1993, Lu 1996).

A weakly connected component of a simple directed graph (i.e., a digraph without loops) is a maximal subdigraph such that for every pair of distinct vertices u, v in the ...

The arithmetic-geometric matrix A_(AG) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=sqrt(d_i^2+d_j^2), (1) where d_i are the vertex degrees of the ...

An independent dominating set of a graph G is a set of vertices in G that is both an independent vertex set and a dominating set of G. The minimum size of an independent ...