Publications (651)698.25 Total impact
 Applied Mathematics and Computation 01/2016; 273:759–766. DOI:10.1016/j.amc.2015.10.047 · 1.55 Impact Factor
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ABSTRACT: Let W, Sz, PI, and WP be, respectively, the Wiener, Szeged, PI, and Wiener polarity indices of a molecular graph G. Let M1 and M2 be the first and second Zagreb indices of G. We obtain relations between these classical distance and degreebased topological indices.Applied Mathematics and Computation 11/2015; 270:142147. DOI:10.1016/j.amc.2015.08.061 · 1.55 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Keywords: Laplacian eigenvalues Laplacian energy Vertex connectivity Edge connectivity Vertex cover number Spanning tree packing number a b s t r a c t For G being a graph with n vertices and m edges, and with Laplacian eigenvalues μ 1 ≥ μ 2 ≥ · · · ≥ μ n−1 ≥ μ n = 0, the Laplacian energy is defined as LE = n i=1 μ i − 2m/n. Let σ be the largest positive integer such that μ σ ≥ 2m/n. We characterize the graphs satisfying σ = n − 1. Using this, we obtain lower bounds for LE in terms of n, m, and the first Zagreb index. In addition, we present some upper bounds for LE in terms of graph invariants such as n, m, maximum degree, vertex cover number, and spanning tree packing number.Applied Mathematics and Computation 10/2015; 268:8392. DOI:10.1016/j.amc.2015.06.064 · 1.55 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In a study on the structuredependency of the total $\pi$electron energy from 1972, Trinajsti\'c and one of the present authors have shown that it depends on the sums $\sum_{v\in V}d(v)^2$ and $\sum_{v\in V}d(v)^3$, where $d(v)$ is the degree of a vertex $v$ of the underling molecular graph $G$. The first sum was later named {\it first Zagreb index} and over the years became one of the most investigated graphbased molecular structure descriptors. On the other hand, the second sum, except in very few works on the general first Zagreb index and the zerothorder general Randi\'c index, has been almost completely neglected. Recently, this second sum was named {\it forgotten index}, or shortly the \F${\it index}, and shown to have an exceptional applicative potential. In this paper we examine the trees extremal with respect to the $F$index.  [Show abstract] [Hide abstract]
ABSTRACT: Applying the Cauchy–Schwarz inequality, we obtain a sharp upper bound on the Randić energy of a bipartite graph and of graphs whose adjacency matrix is partitioned into blocks with constant row sum.Linear Algebra and its Applications 08/2015; 478. DOI:10.1016/j.laa.2015.03.039 · 0.94 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Graph invariants, based on the distances between the vertices of a graph, are widely used in theoretical chemistry. The degree resistance distance of a graph is defined as , where is the degree of the vertex , and the resistance distance between the vertices and . Let be the set of all cacti possessing vertices and cycles. The elements of with minimum degree resistance distance are characterized.Discrete Applied Mathematics 06/2015; 188(1). DOI:10.1016/j.dam.2015.02.022 · 0.80 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Given a graph , the atom–bond connectivity ( ) index is defined to be where and are vertices of , denotes the degree of the vertex , and indicates that and are adjacent. Although it is known that among trees of a given order , the star has maximum index, we show that if , then the star of order has minimum index among trees with leaves. If , then the balanced double star of order has the smallest index.Discrete Applied Mathematics 05/2015; 194. DOI:10.1016/j.dam.2015.05.008 · 0.80 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The resolvent Estrada index of a (noncomplete) graph $G$ of order $n$ is defined as $EE_r =\sum_{i=1}^n(1\lamda_i/(n1))^{1}$, where $\lamda_1, \lamda_2, \lamda_n$ are the eigenvalues of $G$. Combining computational and mathematical approaches, we establish a number of properties of $EE_r$. In particular, any tree has smaller $EE_r$value than any unicyclic graph of the same order, and any unicyclic graph has smaller $EE_r$value than any tricyclic graph of the same order. The trees, unicyclic, bicyclic, and tricyclic graphs with smallest and greatest $EE_r$ are determined.MATCH Communications in Mathematical and in Computer Chemistry 05/2015; 74:431440. · 1.47 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In a recent paper [H. Lin,MATCHCommunications in Mathematical and in Computer Chemistry 70 (2013) 575–582], a congruence relation forWiener indices of a class of trees was reported. We now show that Lin’s congruence is a special case of a much more general result.Filomat 05/2015; 29(5):10811083. · 0.64 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A direct method for computation of the energyeffect (ef) of cycles in conjugated molecules is elaborated, based on numerical calculation of the (complex) zeros of certain graph polynomials. Accordingly, the usage of the Coulson integral formula can be avoided, and thus the efvalues can be calculated for arbitrary cycles of arbitrary conjugated systems.Journal of Mathematical Chemistry 04/2015; 53(4). DOI:10.1007/s109100150473y · 1.15 Impact Factor 
Article: A forgotten topological index
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ABSTRACT: In 1972, within a study of the structuredependency of total \(\pi \) electron energy ( \({\mathcal {E}}\) ), it was shown that \({\mathcal {E}}\) depends on the sum of squares of the vertex degrees of the molecular graph (later named first Zagreb index), and thus provides a measure of the branching of the carbonatom skeleton. In the same paper, also the sum of cubes of degrees of vertices of the molecular graph was shown to influence \({\mathcal {E}}\) , but this topological index was never again investigated and was left to oblivion. We now establish a few basic properties of this “forgotten topological index” and show that it can significantly enhance the physicochemical applicability of the first Zagreb index.Journal of Mathematical Chemistry 04/2015; 53(4). DOI:10.1007/s109100150480z · 1.15 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Benzenoid molecules possessing bays are traditionally considered as “strain–free”. Yet, repulsion between the two bay Hatoms affects the length of the nearlying carbon–carbon bonds. A method is developed to estimate the energy of this strain. In the case of phenanthrene its value was found to be about 7 kJ/mol.Chemical Physics Letters 02/2015; 625. DOI:10.1016/j.cplett.2015.02.039 · 1.90 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The graphs and trees with smallest resolvent Estrada indices (EEr) are characterized. The connected graph of order n with smallest EErvalue is the nvertex path. The secondsmallest such graph is the (n1)vertex path with a pendent vertex attached at position 2. The tree with thirdsmallest EEr is the (n1)vertex path with a pendent vertex attached at position 3, conjectured to be also the connected graph with thirdsmallest EEr. Based on a computeraided search, we established the structure of a few more trees with smallest EEr.MATCH Communications in Mathematical and in Computer Chemistry 01/2015; 73(1):267270. · 1.47 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Inarecentpaper[H.Lin,MATCHCommunicationsinMathematicalandinComputerChemistry 70 (2013) 575–582], a congruence relation for Wiener indices of a class of trees was reported. We now show that Lin’s congruence is a special case of a much more general result.Filomat 01/2015; 29(5):10811083. DOI:10.2298/FIL1505081G · 0.64 Impact Factor 
Article: Borderenergetic graphs
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ABSTRACT: The energy ε(G) of a graph G is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. A graph G of order n is said to be borderenergetic if its energy equals the energy of the complete graph Kn , i.e., if ε(G) = 2(n  1). We first show by examples that there exist connected borderenergetic graphs, different from the complete graph Kn . The smallest such graph is of order 7. We then show that for each integer n , n ≥ 7, there exists borderenergetic graphs of order n, different from Kn , and describe the construction of some of these graphs.  [Show abstract] [Hide abstract]
ABSTRACT: For a simple connected graph G of order n, the Laplacianenergylike invariant and the Kirchhoff index are calculated by LEL(G) = Sigma(n1)(i=1) root mu(i); and K f(G) = n Sigma(n1)(i=1) 1/mu(i), respectively, where mu(1,)mu 2,....,mu(n1),mu(n)= 0 are the Laplacian eigenvalues of G. We obtain a sharp upper bound for K f and a sharp lower bound for LEL. Further, we obtain upper and lower bounds for LEL and K f for graphs C(G) (the cliqueinserted graph or paraline graph), R(G) (obtained by changing each edge of G into a triangle), and H(G) (obtained by inserting a new vertex on each edge of G and by joining two new vertices if they lie on adjacent edges of G), as well as for the line graph of a semiregular graph.MATCH Communications in Mathematical and in Computer Chemistry 01/2015; 73(1):4159. · 1.47 Impact Factor  Journal of the Serbian Chemical Society 01/2015; DOI:10.2298/JSC150126015G · 0.87 Impact Factor

Article: On Randic Energy
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ABSTRACT: Let G be a simple graph with n vertices and m edges. Let d(i) be the degree of the ith vertex of G. The Randic matrix R = (r(ij)) is defined by r(ij) = 1/root d(i)d(j) if the ith and jth vertices are adjacent and r(ij) = 0 otherwise. The Randic energy RE is the sum of absolute values of the eigenvalues of R. Cavers at al. [On the normalized Laplacian energy and general Randic index R1(G) of graphs, Lin. Algebra Appl. 433 (2010) 172190] obtained some bounds on RE, but did not characterize the extremal graphs. We now find these extremal graphs. Additional lower and upper bounds for RE are obtained, in terms of n, m, maximum degree Delta, minimum degree delta, and the determinant of the adjacency matrix.MATCH Communications in Mathematical and in Computer Chemistry 01/2015; 73(1):8192. · 1.47 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Given a graph G, the atombond connectivity (ABC) index is defined to be ABC(G) = Σuv∈E(G) √ dG(u)+dG(v)2/dG(u) dG(v) , where E(G) is the edge set of graph G and dG(v) is the degree of vertex v in graph G. The paper [10] claims to classify tho trees with a fixed number of leaves which minimize the ABC index. Unfortunately, there is a gap in the proof, leading to other examples that contradict the main result of that work. These examples and the problem are discussed in this note.MATCH Communications in Mathematical and in Computer Chemistry 01/2015; 74(3):697701. · 1.47 Impact Factor 
Article: On zagreb indices and coindices
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ABSTRACT: A complete set of relations is established between the first and second Zagreb index and coindex of a graph and of its complements. Formulas for the first Zagreb index of several derived graphs are also obtained. A remarkable result is that the first Zagreb coindices of a graph and of its complement are always equal.
Publication Stats
11k  Citations  
698.25  Total Impact Points  
Top Journals
Institutions

2015

State University of Novi Pazar
Yeni Pazar, Central Serbia, Serbia


19832015

University of Kragujevac
 Department of Chemistry
Krabujevac, Central Serbia, Serbia


20132014

King Abdulaziz University
 Department of Chemistry
Djidda, Makkah, Saudi Arabia


20102011

Tilburg University
 Department of Econometrics & Operations Research
Tilburg, North Brabant, Netherlands


2008

Uzbekistan Academy of Sciences
Toshkent, Toshkent Shahri, Uzbekistan


2004

University of Split
 Department of Mathematics
Spalato, SplitskoDalmatinska, Croatia


2003

Xiamen University
Amoy, Fujian, China


2001

University of Freiburg
 Institute of Organic Chemistry and Biochemistry (Organic Chemistry)
Freiburg, BadenWürttemberg, Germany


20002001

University of the Andes (Venezuela)
 Department of Mathematics
Mérida, Estado Mérida, Venezuela


19941998

University of Szeged
 Institute of Chemistry
Algyő, Csongrád, Hungary


1997

University of Zagreb
 Department of Processes Engineering
Zagrabia, Grad Zagreb, Croatia 
BabeşBolyai University
 Department of Mathematics
Klausenburg, Cluj, Romania


19951997

Hebrew University of Jerusalem
 • Department of Organic Chemistry
 • Department of Inorganic Chemistry
Yerushalayim, Jerusalem, Israel


19721995

Ruđer Bošković Institute
 Department of Physical Chemistry
Zagrabia, Grad Zagreb, Croatia


19931994

Academia Sinica
 Institute of Chemistry
T’aipei, Taipei, Taiwan


1988

Ruder Boskovic Institute
Zagrabia, Grad Zagreb, Croatia
