On the anti-forcing number of benzenoids

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Webstructures.9 Zhang, Ye, and Shiu have found lower bounds for the forcing matching number of fullerenes.10 Vuki cevi c and Trinajsti c have investigated the anti-forcing number of benzenoids, the smallest number of edges that must be removed from a benzenoid so that a single Kekul e structure remains.11 2.2. Independence in Chemistry. Web1 de fev. de 2008 · The notions of a forcing edge and the forcing number of a perfect matching first appeared in a 1991 paper [15] by Harary, Klein an Zivkovi. The root of these concepts can be traced to the works ...

Forcing polynomials of benzenoid parallelogram and its related benzenoids

Web13 de jun. de 2006 · On the Anti-forcing Number of Benzenoids On the Anti-forcing Number of Benzenoids Vukiěević, Damir; Trinajstić, Nenad 2006-06-13 00:00:00 The anti-forcing number is introduced as the smallest number of edges that have to be removed … porsche macan gts test drive

Continuous forcing spectrum of regular hexagonal polyhexes

WebIt is shown that all cata-benzenoids have anti-Kekule number either 2 or 3 and both classes are characterized. The explicit formula for anti-forcing number of chain (unbranched) cata-benzenoids is given. It is also shown that anti-forcing number of … Web1 de mar. de 2016 · br000135 D. Vukičević, N. Trinajstić, On the anti-Kekulé number and anti-forcing number of cata-condensed benzenoids, J. Math. Chem., 43 (2008) 719-726. br000140 L. Xu, H. Bian, F. Zhang, Maximum forcing number of hexagonal systems, MATCH Commun. Math. Comput. Chem., 70 (2013) 493-500. WebAnti-Kekulé numbers of some chemical graphs were studied, such as a hexagonal system [ 3], the infinite triangular, rectangular and hexagonal grids [ 16], cata-condensed benzenoids [ 18], fullerene graphs [ 20] and cata-condensed phenylenes [ 22]. irish baked goods recipes

Kekule valence structures revisited. Innate degrees of freedom of …

Anti-forcing spectrum of any cata-condensed hexagonal system is ...

Webparticular, we prove that all catacondensed benzenoids and catafused coronoids with n hexagons have the global forcing number equal to n, and that for pericondensed benze- noids the global forcing number is always strictly smaller than the number of hexagons. KEY WORDS: global forcing number, benzenoid graph WebOn the Anti-Kekulé Number and Anti-Forcing Number of Cata-Condensed Benzenoids. J. Math. Chem. 43, 719–726 (2008) CrossRef MathSciNet MATH Google Scholar Vukičević, D., Trinajstić, N.: On the Anti-Forcing Number of Benzenoids. J. Math. Chem. 42, 575–583 (2007) CrossRef MathSciNet MATH Google Scholar irish baileys fudge recipeWebLet G be a plane elementary bipartite graph with more than one finite face. We first characterize forcing edges and anti-forcing edges of G in terms of handles and forcing faces. We then introduce the concept of a nice pair of faces of G, which allows ... irish bakery names

"Web40) D. Vukičević and N. Trinajstić, On the anti-Kekule number and anti-forcing number of cata-condensed benzenoids, J. Math. Chem, 43 (2) (2008) 719-726. 41) Alexandru T. Balaban, Milan Randić, and Damir Vukičević, Partition of π-Electrons between Faces of Polyhedral Carbon Aggregates, J. Math. Chem. 43 (2) (2008) 773-779. " - On the anti-forcing number of benzenoids

On the anti-forcing number of benzenoids

WebThe anti-forcing number of G is the smallest number of edges whose removal from G results in a subgraph with a unique perfect matching, denoted by of (G). In this paper, we obtain that for a (3, 6)-fullerene graph G, f (G) >= 1 and af(G) >= 2, and any equality holds if and only if it either has connectivity 2 or is isomorphic to K-4. WebFor individual Kekule valence structures we consider the smallest possible number of placements of CC double bonds such that a Kekule structure is fully determined. The number may be viewed as special weighting scheme for individual Kekule valence structures. Alternatively its reciprocal indicates the degree of a long-range order in a …

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WebPreviously introduced concepts the anti-Kekule number and anti-forcing number (Vukicevic et al., J. Math. chem., in press) are applied to cata-condensed benzenoids. It is shown that all cata-benzenoids have anti-Kekule number either 2 or 3 and both classes … WebThe anti-forcing number is introduced as the smallest number of edges that have to be removed that any benzenoid remains with a single Kekulé structure. Similarly, the anti- Kekulé number is discussed as the smallest number of edges that have to be removed …

Web18 de dez. de 2024 · The initial set S is called a forcing set (zero forcing set) of G if, by iteratively applying the forcing process, every vertex in G becomes colored. The zero forcing number of G, denoted Z(G), is the minimum cardinality of a zero forcing set of … Web5 de jul. de 2016 · In particular, for all benzenoid systems, recently Xu et al. [22] showed that the maximum forcing number is equal to the Clar number, and Lei et al. [13] showed that the maximum anti-forcing number is equal to the Fries number. Both indices can measure the stability of benzenoid hydrocarbons. We may refer to a survey [2] on this topic.

WebThe anti-forcing number is introduced as the smallest number of edges that have to be removed that any benzenoid remains with a single Kekul´e structure. Similarly, the anti- Kekul´e number is discussed as the smallest number of edges that have to be removed … WebWe define the anti-forcing number of a perfect matching M of a graph G as the minimal number of edges of G whose deletion results in a subgraph with a unique perfect matching M , denoted by a f ( G , M ) . The anti-forcing number of a graph proposed by ...

WebWe show that the maximum forcing number of G is equal to its Clar number, and the maximum anti-forcing number of G is equal to its Fries number, which extend the known results for hexagonal systems with a perfect matching (Xu etal., 2013; Lei etal., 2016).

WebPDF Previously introduced concepts the anti-Kekule number and anti-forcing number (Vukicevic et al., J. Math. chem., in press) are applied to cata-condensed benzenoids. It is shown that all cata-benzenoids have anti-Kekule number either 2 or 3 and both classes are characterized. The explicit formula for anti-forcing number of chain (unbranched) … porsche macan houstonWebIn this paper we consider some specific graphs that are of importance in chemistry and study their anti-forcing numbers. Toggle navigation. Home; Browse . Current Issue; By Issue; By Author; By Subject; Author Index; Keyword Index; Journal Info . About Journal; Aims and Scope; Editorial Board; porsche macan hybrid fiche techniqueWebPreviously introduced concepts the anti-Kekule number and anti-forcing number´ (Vukicevic et al., J. Math. chem., in press) are applied to cata-condensed benze-noids. It is shown that all cata-benzenoids have anti-Kekul´e number either 2 or 3 and both … irish bakeryWebJournal of Mathematical Chemistry, Vol. 43, No. 2, February 2008 (© 2007) DOI: 10.1007/s10910-006-9223-5 On the anti-Kekul´e number and anti-forcing number of cata-condensed benzenoids Damir Vukiˇcevi´c∗ and Nenad Trinajsti´c Department of … porsche macan hurenWebPreviously introduced concepts the anti-Kekulé number and anti-forcing number (Vukicevic et al., J. Math. chem., in press) are applied to cata-condensed benzenoids. It is shown that all cata-benzenoids have anti-Kekulé number either 2 or 3 and both classes … irish bakery quincy maWeb5 de jul. de 2016 · In particular, for all benzenoid systems, recently Xu et al. [22] showed that the maximum forcing number is equal to the Clar number, and Lei et al. [13] showed that the maximum anti-forcing number is equal to the Fries number. Both indices can measure the stability of benzenoid hydrocarbons. We may refer to a survey [2] on this topic. irish bakery barrington ilWebDownloadable (with restrictions)! Klein and Randić introduced the innate degree of freedom (forcing number) of a Kekulé structure (perfect matching) M of a graph G as the smallest cardinality of subsets of M that are contained in no other Kekulé structures of G, and the innate degree of freedom of the entire G as the sum over the forcing numbers of all … irish baking products