There has been an upsurge of research on complex networks in recent years. The purpose this paper is to study the mathematical properties random pentagonal chain PE C n with help graph theory. Based id="M2"> , we first obtain expected value expressions Gutman in...

The Wiener Index, or the Wiener Number, also known as the “sum of distances” of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and chemical properties, and has been studied in depth. An index proposed by Schultz is shown to be related to the Wiener Index for trees, and Ivan Gutman proposed a modification of the Schultz index with...

The development by Smithies (1955a) of starch gel as a medium for the electrophoresis of protein material marked an important advance, as it combines separation by electrical mobility with a form of pore filtration. Smithies (1955b) has been able to obtain 12 or more protein fractions from human serum with his one-dimensional technique and equally remarkable separation has been obtained with an...

Several relations between the coefficients of the permanental and characteristic polynomials were given by Gutman and Cash [ MATCH Commun. Math. Comput. Chem. 45 (2002) 55-70]. In this paper, some more and general connections between those coefficients are presented.

Let G be a graph. Denote by L(G) its i-iterated line graph and denote by W (G) its Wiener index. Dobrynin, Entringer and Gutman stated the following problem: Does there exist a non-trivial tree T and i ≥ 3 such that W (L(T )) = W (T )? In a series of five papers we solve this problem. In a previous paper we proved that W (L(T )) > W (T ) for every tree T that is not homeomorphic to a path, claw...

A numeric parameter which studies the behaviour, structural, toxicological, experimental, and physicochemical properties of chemical compounds under several graphs’ isomorphism is known as topological index. In 2018, Ali Trinajsti? studied first Zagreb connection index Z ...

Let G be a graph with vetex set V (G) and edge set E(G). The first generalized multiplicative Zagreb index of G is ∏ 1,c(G) = ∏ v∈V (G) d(v) , for a real number c > 0, and the second multiplicative Zagreb index is ∏ 2(G) = ∏ uv∈E(G) d(u)d(v), where d(u), d(v) are the degrees of the vertices of u, v. The multiplicative Zagreb indices have been the focus of considerable research in computational ...