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
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
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
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.
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.
