On the anti-forcing number of benzenoids

Author: jhmr

August undefined, 2024

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 … 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 Semantic Scholar

Web13 de jun. de 2006 · The 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 … WebLet 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 ... signature hardware lindsey freestanding tub

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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]. 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. 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. signature hardware hurston pot filler

On the maximum forcing and anti-forcing numbers of (4,6) …

On the Anti-forcing Number of Benzenoids - DeepDyve

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). Web24 de mar. de 2006 · Global Forcing Number of Benzenoid Graphs Global Forcing Number of Benzenoid Graphs Došlić, Tomislav 2006-03-24 00:00:00 Journal of Mathematical Chemistry, Vol. 41, No. 3, April 2007 (© 2006) DOI: 10.1007/s10910-006-9056-2 Tomislav Dosli ˇ c´ Department of Informatics and Mathematics, Faculty of … the project tenplayWebparticular, 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 the project terminated

"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. " - On the anti-forcing number of benzenoids

On the anti-forcing number of benzenoids

WebDownloadable (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 … Web3 de nov. de 2016 · The anti-forcing number of a perfect matching M of a graph G is the minimal number of edges not in M whose removal makes M a unique perfect matching of the resulting graph. ... On the anti-forcing number of benzenoids. J Math Chem, 2007, …

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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) … Web5 de jul. de 2016 · The anti-forcing number of a perfect matching M of a graph G is the minimal number of edges of G not in M whose deletion results in a subgraph with a unique perfect matching M.The maximum anti-forcing number of a benzenoid system H equals …

WebG−S has a unique perfect matching. The cardinality of a smallest anti-forcing set is called the anti-forcing number of G, denoted by af(G). D. Vukiˇcevi´c and N. Trinajsti´c [12, 13] recently introduced the anti-forcing number of graphs and determined the anti-forcing numbers of parallelogram benzenoid and cata-condensed benzenoids. WebWe consider resonance in cata-condensed benzenoids having six and seven fused benzene rings. The resonance relationship between the Kekule valence structures of the molecules is represented by the resonance graphs in which the vertices represent the Kekule valence structures, and the edges, the presence of the quantum chemical …

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 ... WebNational Center for Biotechnology Information

Web15 de jul. de 2024 · The minimum (resp. maximum) anti-forcing number of G is the minimum (resp. maximum) value over anti-forcing numbers of all perfect matchings of G denoted by a f ( G) (resp. A f ( G) ). Lei et al. [16] proved that the maximum anti-forcing numbers of benzenoids are equal to their Fries numbers.

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 … the project team people from differentWebOn 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 signature hardware linear shower drainsWebThe 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 … signature hardware helsinki towel bar signature hardware layne vanityWebe 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 any cata-benzenoid goes up to h/ 2w hereh is the number of … the project team srmWebThe 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 … the project theatreWeb9 de mar. de 2007 · Previously 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 … the project team people