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Let s_k be the number of independent vertex sets of cardinality k in a graph G. The polynomial I(x)=sum_(k=0)^(alpha(G))s_kx^k, (1) where alpha(G) is the independence number, ...

A graph G is said to be locally X, where X is a graph (or class of graphs), when for every vertex v, the graph induced on G by the set of adjacent vertices of V (sometimes ...

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 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 ...

The Wiener sum index WS is a graph index defined for a graph on n nodes by WS=1/2sum_(i=1)^nsum_(j=1)^n((d)_(ij))/((Omega)_(ij)), where (d)_(ij) is the graph distance matrix ...

An apex graph is a graph possessing at least one vertex whose removal results in a planar graph. The set of vertices whose removal results in a planar graph is known as the ...

One would think that by analogy with the matching-generating polynomial, independence polynomial, etc., a cycle polynomial whose coefficients are the numbers of cycles of ...

Let d_G(k) be the number of dominating sets of size k in a graph G, then the domination polynomial D_G(x) of G in the variable x is defined as ...

The classic treatise in geometry written by Euclid and used as a textbook for more than 1000 years in western Europe. An Arabic version The Elements appears at the end of the ...

Let the elliptic modulus k satisfy 0<k^2<1, and the Jacobi amplitude be given by phi=amu with -pi/2<phi<pi/2. The incomplete elliptic integral of the first kind is then ...