Publications (783)792.4 Total impact

Dataset: aleksic gutman petrovic
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ABSTRACT: Let G be a bipartite graph of order n with m edges. The energy E(G) of G is the sum of the absolute values of the eigenvalues of the adjacency matrix A. In 1974, one of the present authors established lower and upper bounds for E(G) in terms of n, m, and detA. Now, more than 40 years later, we correct some details of this result and determine the extremal graphs. In addition, an upper bound on the Laplacian energy of bipartite graphs in terms of n, m, and the first Zagreb index is obtained, and the extremal graphs characterized.  [Show abstract] [Hide abstract]
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.  [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.  [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.  [Show abstract] [Hide abstract]
ABSTRACT: Graph invariants, based on the distances between the vertices of a graph, are widely use' in theoretical chemistry. The degree resistance distance of a graph G is defined as DR (G) = Sigma({u,v}subset of V(G))[d(u) + d(v)]R(u, v), where d(u) is the degree of the vertex u, and R(u, v) the resistance distance between the vertices u and v. Let Cact(n; t) be the set of all cacti possessing n vertices and t cycles. The elements of Cact(n; t) with minimum degree resistance distance are characterized.  [Show abstract] [Hide abstract]
ABSTRACT: Given a graph G, the atom bond connectivity (ABC) index is defined to be ABC(G) = Sigma(u similar to v) root d(u)+d(v)2/d(u)d(v) where u and v are vertices of G, d(u) denotes the degree of the vertex u, and u similar to v indicates that u and v are adjacent. Although it is known that among trees of a given order n, the star has maximum ABC index, we show that if k <= 18, then the star of order k+ 1 has minimum ABC index among trees with k leaves. If k >= 19, then the balanced double star of order k + 2 has the smallest ABC index.  [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.  [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. 

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.  [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. 

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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.  [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.  [Show abstract] [Hide abstract]
ABSTRACT: Let Kn1,(n2),...,(np) denote the complete ppartite graph, p > 1, on n = n(1) + n(2) + ... + n(p) vertices and let n(1) >= n(2) >= ... n(p) >= 0. We show that for a fixed value of n, both the spectral radius and the energy of complete ppartite graphs are minimal for complete split graph CS (n, p  1) and are maximal for Turan graph T (n, p).  [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. 
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.
Publication Stats
14k  Citations  
792.40  Total Impact Points  
Top Journals
Institutions

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


2009

University of Osijek
 Department of Mathematics
Osik, OsječkoBaranjska, Croatia


2008

Uzbekistan Academy of Sciences
Toshkent, Toshkent Shahri, Uzbekistan 
University of Kashan
 Department of Pure Mathematics
Kachan, Isfahan, Iran


2004

University of Split
 Department of Mathematics
Spalato, SplitskoDalmatinska, Croatia


2003

Xiamen University
Amoy, Fujian, China


20002003

University of Maribor
 Chair of Mathematics
Maribor, Maribor, Slovenia


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


19992001

Sambalpur University
 Department of Chemistry
Sambalpore, Odisha, India


1998

University of Malta
LImsida, LImsida, Malta


19941998

University of Szeged
 Institute of Chemistry
Algyő, Csongrád, Hungary


1997

University of Zagreb
 Department of Processes Engineering
Zagrabia, Grad Zagreb, Croatia


19951997

Hebrew University of Jerusalem
 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


1992

Ochanomizu University
 Department of Chemistry
Tōkyō, Japan


1988

Ruder Boskovic Institute
Zagrabia, Grad Zagreb, Croatia


1981

University of Ljubljana
Lubliano, Ljubljana, Slovenia
