The Clar covering polynomial of hexagonal systems I

Zhang, Heping; Zhang, Fuji

doi:10.1016/0166-218x(95)00081-2

Cited by 105 publications

(87 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let S be a subgraph of a toroidal polyhex H(p, q, t) for which each component is either a hexagon or an edge with the end-vertices. Then S is called a Clar cover [26] if S includes all vertices of H(p, q, t); an ideal configuration if S is alternately incident with white and black vertices along any direction of each layer.…”

Section: -And 2-resonancementioning

confidence: 99%

k-resonance in Toroidal Polyhexes*

2005

Self Cite

View full text Add to dashboard Cite

This paper considers the k-resonance of a toroidal polyhex (or toroidal graphitoid) with a string (p, q, t) of three integers (p ≥ 2, q ≥ 2, 0 ≤ t ≤ p − 1). A toroidal polyhex G is said to be k-resonant if, for 1 ≤ i ≤ k, any i disjoint hexagons are mutually resonant, that is, G has a Kekulé structure (perfect matching) M such that these hexagons are M -alternating (in and off M ). Characterizations for 1, 2 and 3-resonant toroidal polyhexes are given respectively in this paper.

show abstract

Section: -And 2-resonancementioning

confidence: 99%

k-resonance in Toroidal Polyhexes*

2005

Self Cite

View full text Add to dashboard Cite

show abstract

“…Most commonly known invariants of such kinds are degree-based topological indices. These are actually the numerical values that correlate the structure with various physical properties, chemical reactivity, and biological activities [1][2][3][4][5]. It is an established fact that many properties such as heat of formation, boiling point, strain energy, rigidity and fracture toughness of a molecule are strongly connected to its graphical structure and this fact plays a synergic role in chemical graph theory.…”

Section: Introductionmentioning

confidence: 99%

Some Invariants of Jahangir Graphs

et al. 2017

View full text Add to dashboard Cite

Abstract:In this report, we compute closed forms of M-polynomial, first and second Zagreb polynomials and forgotten polynomial for Jahangir graphs J n , m for all values of m and n. From the M-polynomial, we recover many degree-based topological indices such as first and second Zagreb indices, modified Zagreb index, Symmetric division index, etc. We also compute harmonic index, first and second multiple Zagreb indices and forgotten index of Jahangir graphs. Our results are extensions of many existing results.

show abstract

“…In these studies, some physico-chemical properties and topological indices are used to predict bioactivity of the chemical compounds [3][4][5][6][7]. Algebraic polynomials have also useful applications in chemistry, such as Hosoya polynomial (also called Wiener polynomial) [8], which Cheminformatics is another emerging field in which quantitative structure-activity (QSAR) and structure-property (QSPR) relationships predict the biological activities and properties of the nanomaterial.…”

Section: Introductionmentioning

confidence: 99%

Some Computational Aspects of Boron Triangular Nanotubes

et al. 2017

View full text Add to dashboard Cite

Abstract:The recent discovery of boron triangular nanotubes competes with carbon in many respects. The closed form of M-polynomial of nanotubes produces closed forms of many degree-based topological indices which are numerical parameters of the structure and, in combination, determine properties of the concerned nanotubes. In this report, we give M-polynomials of boron triangular nanotubes and recover many important topological degree-based indices of these nanotubes. We also plot surfaces associated with these nanotubes that show the dependence of each topological index on the parameters of the structure.

show abstract

The Clar covering polynomial of hexagonal systems I

Cited by 105 publications

References 7 publications

k-resonance in Toroidal Polyhexes*

k-resonance in Toroidal Polyhexes*

Some Invariants of Jahangir Graphs

Some Computational Aspects of Boron Triangular Nanotubes

Contact Info

Product

Resources

About