#### Filter Results:

#### Publication Year

2002

2016

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

Recently introduced Zagreb coindices are a generalization of classical Zagreb indices of chemical graph theory. We explore here their basic mathematical properties and present explicit formulae for these new graph invariants under several graph operations .

We introduce a modification of the Harary index where the contributions of vertex pairs are weighted by the sum of their degrees. After establishing basic mathematical properties of the new invariant, we proceed by finding the extremal graphs and investigating its behavior under several standard graph products.

- Franka Miriam Brückler, Tomislav Došlić, Ante Graovac, Ivan Gutman
- 2011

A new class of distance–based molecular structure descriptors is put forward, aimed at eliminating a general shortcoming of the Wiener and Wiener–type indices, namely that the greatest contributions to their numerical values come from vertex pairs at greatest distance. The Q-indices, considered in this work, consist of contributions of vertex pairs that… (More)

A secondary structure is a planar, labeled graph on the vertex set {1; : : : ; n} having two kind of edges: the segments [i; i + 1], for 1 6 i 6 n − 1 and arcs in the upper half-plane connecting some vertices i; j, i 6 j, where j − i ¿ l, for some ÿxed integer l. Any two arcs must be totally disjoint. We enumerate secondary structures with respect to their… (More)

Valence-weightings are considered for shortest-path distance moments, as well as related weightings for the so-called " Wiener " polynomial. In the case of trees the valence-weighted quantities are found to be expressible as a combination of unweighted quantities. Further the weighted quantities for a so-called " thorny " graph are considered and shown to… (More)

Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic behavior of some combinatorially relevant sequences, such as Motzkin and Schröder numbers, sequences of values of some… (More)

- Tomislav Došlić
- 2005

We establish an explicit formula for the maximum value of the product of parts for partitions of a positive integer into distinct parts (sequence A034893 in the On-Line Encyclopedia of Integer Sequences).