The energy of a graph G as chemical concept leading to HMO theory was introduced by Hückel in 1931 and developed into mathematical interpretation many years later when Gutman 1978 gave his famous definition the sum absolute values eigenvalues adjacency matrix G. One general requirements for any topological index is that similar molecules have close TI values, which called smoothness. To explore...

Randić index is one of the most famous topological graph indices. The energy a was defined more than four decades ago for its molecular applications. classical modeling molecule as sum absolute values all eigenvalues adjacency matrix corresponding to graph. There are several other versions notion obtained using types matrices. In this paper, we introducing and investigating type Hadi RHE(G) G, ...

abstract let ‎g=(v,e) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎v‎‎‎ ‎and ‎edge ‎set ‎‎‎e. ‎the szeged index ‎of ‎‎g is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎g ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎if ‎‎‎‎s ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎v ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎s ‎of ‎size ‎3. ‎then ‎we ‎define ‎three ‎...