Total number of papers on ( Thursday, August 28, 2025 ) is 11.
Bojana Borovićanin, Kinkar Ch. Das, Boris Furtula, Ivan Gutman
Zagreb Indices: Bounds and Extremal Graphs
in: Ivan Gutman, Boris Furtula, Kinkar C. Das, Emina Milovanović, Igor Milovanović (Eds.)
Bounds in Chemical Graph Theory - Basics
Faculty of Science, University of Kragujevac, Kragujevac, 2017, pp. 67-153.
About chapter
This chapter surveys results on upper and lower bounds for the first and second Zagreb indices.
Ivan Gutman, Boris Furtula, Emir Zogić, Edin Glogić
Resolvent energy
in: Ivan Gutman, Xueliang Li (Eds.)
Energies of Graphs - Theory and Applications
Faculty of Science, University of Kragujevac, Kragujevac, 2016, pp. 277-290.
About chapter
This chapter introduces a concept of the resolvent energy of graphs. Some features of this quantity are outlined.
Ivan Gutman, Boris Furtula
Metric-extremal graphs
in: Matthias Dehmer, Frank Emmert–Streib (Eds.)
Quantitative Graph Theory: Mathematical Foundations and Applications
CRC Press, Boca Raton, 2014, pp. 111-139.
About chapter
A graph is a mathematical object defined as an ordered pair \( (V ,E) \) of sets \( V \) and \( E \), where \( V \) is a (finite or infinite) set of some unspecified elements, called vertices, and \( E \) is a set of some (ordered or unordered) pairs of elements of \( V \), called edges. Thus, a graph is an abstract set-theoretical concept. As such, it cannot be viewed as something quantitative. Yet, for most applications of graphs, pertinent numerical indicators are needed, which requires that their structural aspects be quantified (see, for instance, [5,11,16,29,30,33,37,81,91,93,122]). This can be done in many different ways, depending on the nature of the intended application, or on the mathematical apparatus preferred.
Ivan Gutman, Boris Furtula
A survey on terminal Wiener index
in: Ivan Gutman, Boris Furtula (Eds.)
Novel Molecular Structure Descriptors - Theory and Applications
Faculty of Science, University of Kragujevac, Kragujevac, 2010, pp. 173-190.
About chapter
The terminal Wiener index \( TW = TW(G) \) of a graph \( G \) is equal to the sum of distances between all pairs of pendent vertices of \( G \). This distance–based molecular structure descriptor was put forward quite recently [I. Gutman, B. Furtula, M. Petrović, J. Math. Chem. 46 (2009) 522-531]. In this survey we outline the hitherto established properties of \( TW \). In particular, we describe a simple method for computing \( TW \) of trees, characterize the trees with minimum and maximum \( TW \), and provide a formula for calculating \( TW \) of thorn graphs.
Boris Furtula, Ivan Gutman
Geometric-arithmetic indices
in: Ivan Gutman, Boris Furtula (Eds.)
Novel Molecular Structure Descriptors - Theory and Applications
Faculty of Science, University of Kragujevac, Kragujevac, 2010, pp. 137-172.
About chapter
The concept of geometric–arithmetic indices (\( GA \)) was introduced in the chemical graph theory very recently. In spite of this, several papers have already appeared dealing with these indices. The main goal of this survey is to collect all hitherto obtained results on \( GA \) indices (both chemical and mathematical).
Jelena Đurđević, Boris Furtula, Ivan Gutman, Slavko Radenković, Sonja Stanković
Comparative study of cyclic conjugation in tribenzoperylene isomers
in: Ante Graovac, Ivan Gutman, Damir Vukičević (Eds.)
Mathematical Methods and Modelling for Students of Chemistry and Biology
Hum, Zagreb, 2009, pp. 29-39.
About chapter
The energy-effects of the 255 different cyclic conjugation modes of three isomeric octacyclic benzenoid hydrocarbons, namely of tribenzo[b,n,pqr]perylene, tribenzo[b,k,pqr]perylene and tribenzo[b,ghi,n]perylene, are calculated by means of a recently developed molecular-orbital-based method. From these energy-effects one can better understand which structural details are responsible for the thermodynamic stability of the underlying molecules. In particular, it is possible to rationalize (in a quantitative manner) the causes of differences in the thermodynamic stability of isomers. From these examples we learn how perplexed are the actual interactions of the \( \pi \)-electrons in polycyclic conjugated molecules.
Sabina Gojak, Sonja Stanković, Ivan Gutman, Boris Furtula
Zhang-Zhang polynomial and some of its applications
in: Ivan Gutman (Eds.)
Mathematical Methods in Chemistry
Prijepolje Museum, Prijepolje, 2006, pp. 141-158.
About chapter
The Chinese mathematicians Heping Zhang and Fuji Zhang conceived a combinatorial polynomial associated with benzenoid molecules. This "Zhang–Zhang polynomial" contains information on both Kekulé- and Clar-structure-based characteristics of the underlying benzenoid molecule. We first explain the definition of the Zhang– Zhang polynomial (and the theoretical concepts on which it is based), and then point out some of its applications to resonance energies. A peculiar discovery made by means of the Zhang–Zhang polynomial is that there are substantial differences between the structure dependence of the Dewar resonance energy and the topological resonance energy.
Jelena Đurđević, Boris Furtula, Ivan Gutman, Radmila Kovavčević, Sonja Stanković, Nedžad Turković
Cyclic conjugation in annelated perylenes
in: Ivan Gutman (Eds.)
Mathematical Methods in Chemistry
Prijepolje Museum, Prijepolje, 2006, pp. 101-117.
About chapter
Cyclic conjugation in benzo-annelated perylenes was studied by means of the energy-effects of their six-membered rings. Several currently used models for assessing the extent of cyclic conjugation in benzenoid hydrocarbons, based on Kekulé structures, Clar formulas, or conjugated circuits, predict that there is no cyclic conjugation in the central, "empty", ring of perylene and its annelated derivatives. We show that in some annelated perylenes the extent of cyclic conjugation in the "empty" ring becomes unexpectedly high. Therefore, in the case of these annelated perylenes the Kekulé-structure-based models fail.
Boris Furtula, Ivan Gutman
Partitioning of \( \pi \)–electrons in the rings of benzenoid hydrocarbons using Fries structural formulas
in: Ivan Gutman (Eds.)
Mathematical Methods in Chemistry
Prijepolje Museum, Prijepolje, 2006, pp. 89-100.
About chapter
The recently introduced concept of electron contents (\( EC \)) of the rings in benzenoid hydrocarbons initiated detailed investigations in that area. There are numerous papers considering this particular topic [1-19]. Calculation of electron contents of the rings is based on Kekulé structures. In this paper, we propose a new way for distributing \( \pi \)-electrons into the hexagons of benzenoid molecules using Fries structures. In addition, we compared our results with those obtained by original the Randić-Balaban model.
Nedžad Turković, Boris Furtula, Ivan Gutman
Electron and energy content of hexagons in benzenoid hydrocarbons
in: Ivan Gutman (Eds.)
Mathematical Methods in Chemistry
Prijepolje Museum, Prijepolje, 2006, pp. 73-87.
About chapter
In this paper we first define the recently proposed (by Randić and Balaban, in 2004) \( \pi \)-electron content (EC) of hexagons in benzenoid hydrocarbons. In full analogy to it one may conceive also the \( \pi \)-electron energy content (ec) of hexagons. These contents are mutually related, but in a somewhat perplexed manner. We establish the actual relation between EC and ec in the case of catacondensed benzenoid hydrocarbons. In catacondensed benzenoid systems there are only four types of hexagons: terminal, linearly annelated, angularly annelated, and branched. We show that within hexagons of the same type the relation between ec and EC is nearly linear and the respective regression lines are nearly parallel and equidistant. The analogous relations between EC and ec in pericondensed benzenoids are essentially the same, yet significantly more complicated because in pericondensed benzenoids there exist 12 distinct annelation modes of hexagons.
Sabina Gojak, Ivan Gutman, Boris Furtula
On distribution of \( \pi \)–electrons in double linear hexagonal chains
in: Ivan Gutman (Eds.)
Mathematical Methods in Chemistry
Prijepolje Museum, Prijepolje, 2006, pp. 63-72.
About chapter
In double linear hexagonal chains the distribution of \( \pi \)-electrons into rings (as computed by means of the Randić–Balaban method) is highly non-uniform: The electron contents monotonically decrease along each polyacene chain. As a somewhat surprising result we show that the sum of \( \pi \)-electron contents of two adjacent rings, belonging to different polyacene chains of the double chain is constant, irrespective of the nature of the terminal fragments. This regularity is a proper generalization of what earlier was observed for single linear hexagonal chains (polyacenes), and is not extendible to triple, quadruple, etc. linear hexagonal chains.