نتایج جستجو برای: catacondensed benzenoid graph

تعداد نتایج: 198340  

2005
H. Hosoya H. Kumazaki K. Chida M. Ohuchi

Various topological factors governing the electronic properties of infinitely large periodic polycyclic benzenoids are analyzed graph-theoretically by drawing the density of states (DS). The existence or non-existence of NBMO's in the hypothetical cyclic dimer of the network are shown to be crucial for the profile of DS. CATAHEXES AND PERIHEXES Owing to the rapid progress in organic synthesis t...

Journal: :Journal of Chemical Information and Computer Sciences 1995
Sandi Klavzar Ivan Gutman Bojan Mohar

It is shown that the vertices of benzenoid systems admit a labeling which reflects their distance relations. To every vertex of a molecular graph of a benzenoid hydrocarbon a sequence of zeros and ones (a binary number) can be associated, such that the number of positions in which these sequences differ is equal to the graph-theoretic vertex distance. It is shown by an example that such labelin...

Journal: :Discrete Mathematics 2006
Khaled Salem Sandi Klavzar Ivan Gutman

The resonance graph R(B) of a benzenoid graph B has the perfect matchings of B as vertices, two perfect matchings being adjacent if their symmetric difference forms the edge set of a hexagon of B . A family P of pair-wise disjoint hexagons of a benzenoid graph B is resonant in B if B−P contains at least one perfect matching, or if B − P is empty. It is proven that there exists a surjective map ...

Journal: :iranian journal of mathematical chemistry 2016
s.-j. xu q.-h. he s. zhou w. h. chan

let $g$ be a molecular graph with vertex set $v(g)$, $d_g(u, v)$ the topological distance between vertices $u$ and $v$ in $g$. the hosoya polynomial $h(g, x)$ of $g$ is a polynomial $sumlimits_{{u, v}subseteq v(g)}x^{d_g(u, v)}$ in variable $x$. in this paper, we obtain an explicit analytical expression for the expected value of the hosoya polynomial of a random benzenoid chain with $n$ hexagon...

Journal: :Computers & chemistry 2000
Sandi Klavzar Petra Zigert Ivan Gutman

An algorithm for the calculation of the hyper-Wiener index (WW) of benzenoid hydrocarbons (both cata- and pericondensed) is described, based on the consideration of pairs of elementary cuts of the corresponding benzenoid graph B. A pair of elementary cuts partitions the vertices of B into four classes. WW is expressed as a sum of terms of the form n11n22 + n12n21, each associated with a pair of...

Journal: :Discrete Applied Mathematics 1996
Douglas J. Klein H.-Y. Zhu

The phenomenon of resonance amongst a set of different classical chemical structures entails at an elementary level the enumeration of these resonance structures, corresponding (in benzenoid molecules) to perfect matchings of the underlying molecular (n-network) graph. This enumeration is analytically performed here for the finite-sized elemental benzenoid graphs corresponding to hexagonal cove...

Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagon...

Journal: :Discussiones Mathematicae Graph Theory 2012
Andrej Taranenko Aleksander Vesel

As a general case of molecular graphs of benzenoid hydrocarbons, we study plane bipartite graphs with Kekulé structures (1-factors). A bipartite graph G is called elementary if G is connected and every edge belongs to a 1-factor of G. Some properties of the minimal and the maximal 1-factor of a plane elementary graph are given. A peripheral face f of a plane elementary graph is reducible, if th...

Journal: :iranian journal of mathematical chemistry 2010
p. e. john s. aziz p. v. khadikar

structural codes vis-a-vis structural counts, like polynomials of a molecular graph, areimportant in computing graph-theoretical descriptors which are commonly known astopological indices. these indices are most important for characterizing carbon nanotubes(cnts). in this paper we have computed sadhana index (sd) for phenylenes and theirhexagonal squeezes using structural codes (counts). sadhan...

Journal: :Discrete Applied Mathematics 1997
Wen-Chung Huang Bo-Yin Yang Yeong-Nan Yeh

An explicit, non-recursive formula for the Wiener index of any given benzenoid chain is derived, greatly speeding up calculations and rendering it manually manageable, through a novel envisioning of chains as ternary strings. Previous results are encompassed and two completely new and useful ones are obtained, a formula to determine Wiener indices of benzenoid chains in periodic patterns, and a...

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