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...

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 ...

The degree distance of a graph G is     , 1 1 1 2 n n i j i i j D G d d L        j , where and i d j d are the degrees of vertices , and is the distance between them. The Wiener index is defined as   , i j v v V G  , i j L   , 1 1 1 2 n n i j i j W G L      . An elegant result (Gutman; Klein, Mihalić,, Plavšić and Trinajstić) is known regarding their correlation, that   ...

Given a complex m n matrix A; we index its singular values as 1 (A) 2 (A) ::: and call the value E (A) = 1 (A)+ 2 (A)+ ::: the energy of A; thereby extending the concept of graph energy, introduced by Gutman. Koolen and Moulton proved that E (G) (n=2) (1 + p n) for any graph G of order n and exhibited an in…nite family of graphs with E (G) = (v (G) =2) 1 + p v (G) . We prove that for all su¢ ci...

Delineation of aquatic plants and estimation of its surface extent are crucial to the efficient control of its proliferation, and this information can be derived accurately with fine resolution remote sensing products. However, small swath and low observation frequency associated with them may be prohibitive for application to large water bodies with rapid proliferation and dynamic floating aqu...

Many tissues contain enzymes which will hydrolyse the organic phosphorus compounds to give free phosphoric acid. These enzymes are known as phosphatases. Some of these phosphatases are most active in an alkaline medium and the others in an acid medium. The phosphatase of bone (Yamane, 1931), bile (King and Armstrong, 1934) and white blood cells (Roche, 1931) are alkaline phosphatases, while tho...

The atom-bond connectivity (ABC) index is one of the most investigated degreebased molecular structure descriptors with a variety of chemical applications. It is known that among all connected graphs, the trees minimize the ABC index. However, a full characterization of trees with a minimal ABC index is still an open problem. By now, one of the proved properties is that a tree with a minimal AB...

I. Gutman, J. H. Koolen, V. Moulton, M. Parac, T. Soldatović, and D. Vidović Faculty of Science, University of Kragujevac, P. O. Box 60, YU-34000 Kragujevac, Yugoslavia a FSPM-Strukturbildungsprozesse, University of Bielefeld, D-33501 Bielefeld, Germany b Physics and Mathematics Department (FMI), Mid Sweden University, Sundsvall, S-85170, Sweden c Faculty of Physical Chemistry, University of Be...

D. B. Gutman,1,2 S. Tongay,3 H. K. Pal,3 D. L. Maslov,3 and A. F. Hebard3 1Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe, Germany 2DFG–Center for Functional Nanostructures, Universität Karlsruhe, 76128 Karlsruhe, Germany 3Department of Physics, University of Florida, Gainesville, Florida 32611, USA Received 21 March 2009; revised manuscript received 2 Ju...