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The Wiener index and the Szeged index of benzenoid systems in linear time
 J. Chem. Inf. Comput. Sci
, 1997
"... A linear time algorithm is presented which, for a given benzenoid system G, computes the Wiener index of G. The algorithm is based on an isometric embedding of G into the Cartesian product of three trees, combined with the notion of the Wiener index of vertexweighted graphs. An analogous approach y ..."
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A linear time algorithm is presented which, for a given benzenoid system G, computes the Wiener index of G. The algorithm is based on an isometric embedding of G into the Cartesian product of three trees, combined with the notion of the Wiener index of vertexweighted graphs. An analogous approach yields also a linear algorithm for computing the Szeged index of benzenoid systems. 1.
CHEMICAL GRAPH THEORY OF FIBONACENES
"... Fibonacenes (zigzag unbranched catacondensed benzenoid hydrocarbons) are a class of polycyclic conjugated systems whose molecular graphs possess remarkable properties, often related with the Fibonacci numbers. This article is a review of the chemical graph theory of fibonacenes, with emphasis on th ..."
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Fibonacenes (zigzag unbranched catacondensed benzenoid hydrocarbons) are a class of polycyclic conjugated systems whose molecular graphs possess remarkable properties, often related with the Fibonacci numbers. This article is a review of the chemical graph theory of fibonacenes, with emphasis on their Kekulé–structure–related and Clar–structure–related properties.
On the Estimation of PI index of Polyacenes
 Acta Chim. Slov. 2002
"... This paper is dedicated to Professor Ivan Gutman, teacher, inspirer, friend, and proprietor of graph theory and topology. ..."
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This paper is dedicated to Professor Ivan Gutman, teacher, inspirer, friend, and proprietor of graph theory and topology.
Distances in Benzenoid Systems: Further Developments
, 1998
"... We present some new results on distances in benzenoids. An algorithm is proposed which, for a given benzenoid system G bounded by a simple circuit Z with n vertices, computes the Wiener index of G in O(n) number of operations. We also show that benzenoid systems have a convenient dismantling scheme, ..."
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Cited by 4 (0 self)
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We present some new results on distances in benzenoids. An algorithm is proposed which, for a given benzenoid system G bounded by a simple circuit Z with n vertices, computes the Wiener index of G in O(n) number of operations. We also show that benzenoid systems have a convenient dismantling scheme, which can be derived by applying the breadthfirst search to their dual graphs. Our last result deals with the clustering problem of sets of atoms of benzenoids systems. We demonstrate how the
FIBONACCI CUBES ARE THE RESONANCE GRAPHS OF FIBONACCENES
, 2003
"... Fibonacci cubes were introduced in 1993 and intensively studied afterwards. This paper adds the following theorem to these studies: Fibonacci cubes are precisely the resonance graphs of fibonaccenes. Here fibonaccenes are graphs that appear in chemical graph theory and resonance graphs reflect the s ..."
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Cited by 3 (1 self)
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Fibonacci cubes were introduced in 1993 and intensively studied afterwards. This paper adds the following theorem to these studies: Fibonacci cubes are precisely the resonance graphs of fibonaccenes. Here fibonaccenes are graphs that appear in chemical graph theory and resonance graphs reflect the structure of their perfect matchings. Some consequences of the main result are also listed.
Situ Chemical Oxidation of Creosote/Coal Tar Residuals: Experimental and Numerical Investigation
, 2004
"... I herby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final version, as accepted by my examiners. I understand that my thesis may be made electronically available to the public ..."
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I herby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final version, as accepted by my examiners. I understand that my thesis may be made electronically available to the public
A MinMax Result on Catacondensed Benzenoid Graphs
, 2001
"... The resonance graph of a benzenoid graph G has the 1factors of G as vertices, two 1factors being adjacent if their symmetric difference forms the edge set of a hexagon of G. It is proved that the smallest number of elementary cuts that cover a catacondensed benzenoid graph equals the dimension of ..."
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The resonance graph of a benzenoid graph G has the 1factors of G as vertices, two 1factors being adjacent if their symmetric difference forms the edge set of a hexagon of G. It is proved that the smallest number of elementary cuts that cover a catacondensed benzenoid graph equals the dimension of a largest induced hypercube of its resonance graph.
Wiener Number of Hexagonal Bitrapeziums and Trapeziums
 Bull. Acad. Serbe Sci. Arts (Cl. Sci. Math. Natur
, 1997
"... The Wiener number of a connected graph is equal to the sum of distances between all pairs of its vertices. A graph formed by a row of n hexagonal cells is called an nhexagonal chain. A graph consisting of m shexagonal chains, where s runs from n to n \Gamma m+1 , forming the shape of a trapezium ..."
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The Wiener number of a connected graph is equal to the sum of distances between all pairs of its vertices. A graph formed by a row of n hexagonal cells is called an nhexagonal chain. A graph consisting of m shexagonal chains, where s runs from n to n \Gamma m+1 , forming the shape of a trapezium is called an n \Theta m hexagonal trapezium. A graph obtained by merging the base nhexagonal chains of two n \Theta m hexagonal trapeziums, forming a convex 6sided polygram, is called an n \Theta m hexagonal bitrapezium. In this paper, we obtain the Wiener numbers of the n \Theta m hexagonal trapezium and of the n \Theta m hexagonal bitrapezium. Key words and phrases: Wiener number, distance in graphs, hexagonal systems AMS 1991 Subject Classifications: 05C12, 05C90. 1 Introduction An important invariant of connected graphs is called the Wiener number (or Wiener index) W . This number is equal to the sum of distances between all pairs of vertices of the respective graph. The quantity W...
Polyhedral Combinatorics of Benzenoid Problems
 Lect. Notes Comput. Sci
, 1998
"... Many chemical properties of benzenoid hydrocarbons can be understood in terms of the maximum number of mutually resonant hexagons, or Clar number, of the molecules. Hansen and Zheng (1994) formulated this problem as an integer program and conjectured, based on computational results, that solving the ..."
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Many chemical properties of benzenoid hydrocarbons can be understood in terms of the maximum number of mutually resonant hexagons, or Clar number, of the molecules. Hansen and Zheng (1994) formulated this problem as an integer program and conjectured, based on computational results, that solving the linear programming relaxation always yields integral solutions. We prove this conjecture showing that the constraint matrices of these problems are unimodular. This establishes the integrality of the relaxation polyhedra since the linear programs are in standard form. However, the matrices are not, in general, totally unimodular as is often the case with other combinatorial optimization problems that give rise to integral polyhedra. Similar results are proved for the Fries number, another optimization problem for benzenoids. In a previous paper, Hansen and Zheng (1992) showed that a certain minimum weight cut cover problem defined for benzenoids yields an upper bound for the Clar number and...