A benzenoid, or a benzenoid system, is a connected planar graph whose every interiorface is a regular hexagon. A peak (resp. valley) of a benzenoid is a vertex which lies above(resp. below) all its first neighbors. A ...A benzenoid, or a benzenoid system, is a connected planar graph whose every interiorface is a regular hexagon. A peak (resp. valley) of a benzenoid is a vertex which lies above(resp. below) all its first neighbors. A Kekulean benzenoid is a benzenoid with at least oneperfect matching. An essentially disconnected benzenoid is a Kekulean benzenoid which hassome fixed bonds. Essentially disconnected benzenoids have proved to be very useful incertain enumeration techniques for Derfect matching. Hence the problem of recognizing展开更多
Jasmine [Jasminum sambac(L.) Ait.], a tropical and subtropical plant emits a sweet, heady fragrance during flower opening. However, the molecular mechanisms underlying this phenomenon remain largely unknown. In the pr...Jasmine [Jasminum sambac(L.) Ait.], a tropical and subtropical plant emits a sweet, heady fragrance during flower opening. However, the molecular mechanisms underlying this phenomenon remain largely unknown. In the present study, integrated Illumina sequencing, Pacbio sequencing, and high-throughput chromatin conformation capture(Hi-C) scaffolding was used to generate a 495.60 Mb genome assembly of J.sambac var. unifoliatum cultivar ‘Fuzhou Single-petal’(JSU-FSP), with contig N50 of 16.88 Mb;96.23% of the assembly was assigned to 13 pseudochromosomes. The genome harbors 30 989 protein-coding genes, and 49.47% of the assembled sequences are repetitive sequences. The analysis of duplication modes showed that 51% of genes were duplicated through dispersed duplication, and expanded gene families are mainly involved in photosynthesis, which may be responsible for the light-loving characteristic specific to jasmine. Transcriptome analysis revealed that at least 35 structural genes involved in the biosynthesis of volatile terpenes(VTs), volatile phenylpropanoid/benzenoids(VPBs),fatty acid-derived volatiles(FADVs), and indole were highly expressed in the flower-opening stage, both preharvest and postharvest, and are proposed to be important in endowing flower aroma. Additionally, at least 28 heat shock protein(HSP) and 11 β-glucosidase(BGLU) genes may be involved in the formation of floral fragrance. These findings provide insights into the formation of the floral fragrance of jasmine and will promote germplasm utilization for breeding improved jasmine varieties.展开更多
Let G = (V;E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V(G) and E = E(G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. ...Let G = (V;E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V(G) and E = E(G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The Sanskruti index S(G) is a topological index was defined as where Su is the summation of degrees of all neighbors of vertex u in G. The goal of this paper is to compute the Sanskruti index for circumcoronene series of benzenoid.展开更多
We consider a series of benzenoid isomers obtained by attaching fragments to an mradical. Some of their topological properties, such as the number of Kekule patterns and the maximum number of aromatic π-sextets are e...We consider a series of benzenoid isomers obtained by attaching fragments to an mradical. Some of their topological properties, such as the number of Kekule patterns and the maximum number of aromatic π-sextets are established.展开更多
We study a random planar honeycomb lattice model, namely the random double hexagonal chains. This is a lattice system with nonperiodic boundary condition. The Wiener number is an important molecular descriptor based o...We study a random planar honeycomb lattice model, namely the random double hexagonal chains. This is a lattice system with nonperiodic boundary condition. The Wiener number is an important molecular descriptor based on the distances, which was introduced by the chemist Harold Wiener in 1947. By applying probabilistic method and combinatorial techniques we obtained an explicit analytical expression for the expected value of Wiener number of a random double hexagonal chain, and the limiting behaviors on the annealed entropy of Wiener number when the random double hexagonal chain becomes infinite in length are analyzed.展开更多
Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg<sub>1</...Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg<sub>1</sub>(G,x) and Zg<sub>1</sub>(G) of the graph G are defined as Σ<sub>uv∈E(G)</sub>x<sup>(d<sub>u</sub>+d<sub>v</sub>)</sup> and Σ<sub>e=uv∈E(G)</sub>(d<sub>u</sub>+d<sub>v</sub>) respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Zagreb index as Zg<sub>1</sub>*</sup>=Σ<sub>uv∈E(G)</sub>(ecc(v)+ecc(u)), that ecc(u) is the largest distance between u and any other vertex v of G. In this paper, we compute this new index (the first Eccentric Zagreb index or third Zagreb index) of an infinite family of linear Polycene parallelogram of benzenoid.展开更多
For a Kekulean benzenoid system, we can define the fixed single bonds, fixed double bonds and forcing bounds. The first and second types of bonds can be recognized by efficient algorithms.In this paper, we give an eff...For a Kekulean benzenoid system, we can define the fixed single bonds, fixed double bonds and forcing bounds. The first and second types of bonds can be recognized by efficient algorithms.In this paper, we give an efficient algorithm to recognize the forcing bonds of a benzenoid system.For a cata-condensed benzenoid system we completely determine its forcing bonds. Furthermore,by Polya's theorem we enumerate all cat-condensed benzenoid Systems with forcing bonds.展开更多
In order to study the stability and estimate the resonance energy of benzenoid systems, many chemists agree that some kinds of Kekulé structures are more important than the others. Dewar and Longuet-Higgins, Clar...In order to study the stability and estimate the resonance energy of benzenoid systems, many chemists agree that some kinds of Kekulé structures are more important than the others. Dewar and Longuet-Higgins, Clar, Randi, Randiand Klein gave different kinds of weights to Kekul structures of benzenoid hydrocarbon, respectively. Using their own concept, several approaches are proposed to calculate the resonance energy. In this note we propose an invafiant for benzenoid hydrocarbon, by which展开更多
The Kekulé-based valence bond (VB) method, in which the VB model is solved using covalent Kekulé structures as basis functions, is justified in the present work. This method is demonstrated to provide satisf...The Kekulé-based valence bond (VB) method, in which the VB model is solved using covalent Kekulé structures as basis functions, is justified in the present work. This method is demonstrated to provide satisfactory descriptions for resonance energies and bond lengths of benzenoid hydrocarbons, being in good agreement with SCF-MO and experimental results. In addition, an alternative way of discussing characters of localized substructures within a polycyclic benzenoid system is suggested based upon such simplified VB calculations. Finally, the symmetries of VB ground states for nonalternant conjugated systems are also illustrated to be obtainable through these calculations, presenting very useful information for understanding the chemical behaviors of some nonalternant conjugated molecules.展开更多
文摘A benzenoid, or a benzenoid system, is a connected planar graph whose every interiorface is a regular hexagon. A peak (resp. valley) of a benzenoid is a vertex which lies above(resp. below) all its first neighbors. A Kekulean benzenoid is a benzenoid with at least oneperfect matching. An essentially disconnected benzenoid is a Kekulean benzenoid which hassome fixed bonds. Essentially disconnected benzenoids have proved to be very useful incertain enumeration techniques for Derfect matching. Hence the problem of recognizing
基金supported by the Construction of Plateau Discipline of Fujian Province (Grant No. 102/71201801101)the Construction Project for Technological Innovation and Service System of Tea Industry Chain of Fujian Agriculture and Forestry University (Grant No. K1520005A01)。
文摘Jasmine [Jasminum sambac(L.) Ait.], a tropical and subtropical plant emits a sweet, heady fragrance during flower opening. However, the molecular mechanisms underlying this phenomenon remain largely unknown. In the present study, integrated Illumina sequencing, Pacbio sequencing, and high-throughput chromatin conformation capture(Hi-C) scaffolding was used to generate a 495.60 Mb genome assembly of J.sambac var. unifoliatum cultivar ‘Fuzhou Single-petal’(JSU-FSP), with contig N50 of 16.88 Mb;96.23% of the assembly was assigned to 13 pseudochromosomes. The genome harbors 30 989 protein-coding genes, and 49.47% of the assembled sequences are repetitive sequences. The analysis of duplication modes showed that 51% of genes were duplicated through dispersed duplication, and expanded gene families are mainly involved in photosynthesis, which may be responsible for the light-loving characteristic specific to jasmine. Transcriptome analysis revealed that at least 35 structural genes involved in the biosynthesis of volatile terpenes(VTs), volatile phenylpropanoid/benzenoids(VPBs),fatty acid-derived volatiles(FADVs), and indole were highly expressed in the flower-opening stage, both preharvest and postharvest, and are proposed to be important in endowing flower aroma. Additionally, at least 28 heat shock protein(HSP) and 11 β-glucosidase(BGLU) genes may be involved in the formation of floral fragrance. These findings provide insights into the formation of the floral fragrance of jasmine and will promote germplasm utilization for breeding improved jasmine varieties.
文摘Let G = (V;E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V(G) and E = E(G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The Sanskruti index S(G) is a topological index was defined as where Su is the summation of degrees of all neighbors of vertex u in G. The goal of this paper is to compute the Sanskruti index for circumcoronene series of benzenoid.
文摘We consider a series of benzenoid isomers obtained by attaching fragments to an mradical. Some of their topological properties, such as the number of Kekule patterns and the maximum number of aromatic π-sextets are established.
文摘We study a random planar honeycomb lattice model, namely the random double hexagonal chains. This is a lattice system with nonperiodic boundary condition. The Wiener number is an important molecular descriptor based on the distances, which was introduced by the chemist Harold Wiener in 1947. By applying probabilistic method and combinatorial techniques we obtained an explicit analytical expression for the expected value of Wiener number of a random double hexagonal chain, and the limiting behaviors on the annealed entropy of Wiener number when the random double hexagonal chain becomes infinite in length are analyzed.
文摘Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg<sub>1</sub>(G,x) and Zg<sub>1</sub>(G) of the graph G are defined as Σ<sub>uv∈E(G)</sub>x<sup>(d<sub>u</sub>+d<sub>v</sub>)</sup> and Σ<sub>e=uv∈E(G)</sub>(d<sub>u</sub>+d<sub>v</sub>) respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Zagreb index as Zg<sub>1</sub>*</sup>=Σ<sub>uv∈E(G)</sub>(ecc(v)+ecc(u)), that ecc(u) is the largest distance between u and any other vertex v of G. In this paper, we compute this new index (the first Eccentric Zagreb index or third Zagreb index) of an infinite family of linear Polycene parallelogram of benzenoid.
文摘For a Kekulean benzenoid system, we can define the fixed single bonds, fixed double bonds and forcing bounds. The first and second types of bonds can be recognized by efficient algorithms.In this paper, we give an efficient algorithm to recognize the forcing bonds of a benzenoid system.For a cata-condensed benzenoid system we completely determine its forcing bonds. Furthermore,by Polya's theorem we enumerate all cat-condensed benzenoid Systems with forcing bonds.
基金Project supported by the National Natural Sdence Foundation of China.
文摘In order to study the stability and estimate the resonance energy of benzenoid systems, many chemists agree that some kinds of Kekulé structures are more important than the others. Dewar and Longuet-Higgins, Clar, Randi, Randiand Klein gave different kinds of weights to Kekul structures of benzenoid hydrocarbon, respectively. Using their own concept, several approaches are proposed to calculate the resonance energy. In this note we propose an invafiant for benzenoid hydrocarbon, by which
文摘The Kekulé-based valence bond (VB) method, in which the VB model is solved using covalent Kekulé structures as basis functions, is justified in the present work. This method is demonstrated to provide satisfactory descriptions for resonance energies and bond lengths of benzenoid hydrocarbons, being in good agreement with SCF-MO and experimental results. In addition, an alternative way of discussing characters of localized substructures within a polycyclic benzenoid system is suggested based upon such simplified VB calculations. Finally, the symmetries of VB ground states for nonalternant conjugated systems are also illustrated to be obtainable through these calculations, presenting very useful information for understanding the chemical behaviors of some nonalternant conjugated molecules.
