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The global clustering coefficient C of a graph G is the ratio of the number of closed trails of length 3 to the number of paths of length two in G. Let A be the adjacency ...

A Cayley tree is a tree in which each non-leaf graph vertex has a constant number of branches n is called an n-Cayley tree. 2-Cayley trees are path graphs. The unique ...

The first and second Zagreb indices for a graph with vertex count n and vertex degrees v_i for i=1, ..., n are defined by Z_1=sum_(i=1)^nv_i^2 and Z_2=sum_((i,j) in ...

Zarankiewicz's conjecture asserts that graph crossing number for a complete bipartite graph K_(m,n) is Z(m,n)=|_n/2_||_(n-1)/2_||_m/2_||_(m-1)/2_|, (1) where |_x_| is the ...

The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

The Janko-Kharaghani graphs are two strongly regular graph on 936 and 1800 vertices. They have regular parameters (nu,k,lambda,mu)=(936,375,150,150) and (1800,1029,588,588), ...

A strongly 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 term "God's number" is sometimes given to the graph diameter of Rubik's graph, which is the minimum number of turns required to solve a Rubik's cube from an arbitrary ...

The minimum vertex degree, sometimes simply called the minimum degree, of a graph G is the smallest vertex degree of G, denoted delta.

The rectilinear crossing number of a graph G is the minimum number of crossings in a straight line embedding of G in a plane. It is variously denoted rcr(G), cr^_(G) ...