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The Randić matrix A_(Randic) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=1/(sqrt(d_id_j)), (1) where d_i are the vertex degrees of the graph. In ...

The stability index Z^_(G) of a graph G is defined by Z^_=sum_(k=0)^(|_n/2_|)|c_(2k)|, where c_k is the kth coefficient of the characteristic polynomial and |_n_| denotes the ...

The Weisfeiler-Leman dimension dim_(WL)(G) of a graph G, sometimes known as the WL dimension, is the smallest integer d such that the d-dimensional Weisfeiler-Leman algorithm ...

A set of graph vertices A of a graph with graph edges V is independent if it contains no graph edges.

A graph G is the edge graph of a polyhedron iff G is a simple planar graph which is 3-connected.

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. The most common type of vertex ...

A matching, also called an independent edge set, on a graph G is a set of edges of G such that no two sets share a vertex in common. It is not possible for a matching on a ...

The Harary index of a graph G on n vertices was defined by Plavšić et al. (1993) as H(G)=1/2sum_(i=1)^nsum_(j=1)^n(RD)_(ij), (1) where (RD)_(ij)={D_(ij)^(-1) if i!=j; 0 if ...

As proposed by Hosoya (1971), the Hosoya index (also called Z-index) of a graph is defined by Z = sum_(k=0)^(n)|a_k| (1) = sum_(k=0)^(n)b_k, (2) where n is the number of ...

Let a graph G=(V,E) be defined on vertex set V and edge set E. Then a construction sequence (or c-sequence) for G is a linear order on V union E in which each edge appears ...