On the anti-forcing number of benzenoids
WebPreviously 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 … Web578 D.Vuki ˇeevi ´c and N.Trinajsti ´c/Anti-forcing number of benzenoids Denote by K 0 the Kekule structure that is obtained from´ K0 by rotating three double bonds in the hexagon denoted by circle. Note that K0 and K 0 are two Kekul´e structures on Bm,n–e for each e …
On the anti-forcing number of benzenoids
Did you know?
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 … 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 …
Web10 de jan. de 2007 · 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 ... 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 …
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 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.
WebThe maximum anti-forcing number of a benzenoid system H equals the Fries number of H . Hwang et al. defined the anti-forcing polynomial of a graph as a counting polynomial for perfect matchings with the same anti-forcing number, and obtained explicit expressions of the anti-forcing polynomial of hexagonal chains and crowns.
Web24 de abr. de 2024 · On the anti-Kekulé and anti-forcing number of cata-condensed benzenoids. J. Math. Chem., 43: 719–726 (2008) Article MathSciNet Google Scholar Wang, H., Ye, D., Zhang, H. The forcing number of toroidal polyhexes. J. Math. Chem., 43: 457–475 (2008) Article MathSciNet Google Scholar Yang, Q., Ye, D., Zhang, H., Lin, Y. how fast are bullets in mphWeb9 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 … how fast are cat 5 cablesWebAnti-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]. high country recovery boone ncWeb1 de mar. de 2016 · We 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 ... br000135 D. Vukičević, N. Trinajstić, On the anti-Kekulé number and anti-forcing … high country realty nc banner elk ncWeb15 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. highcountry recycling westcliffe coWebstructures.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. how fast are bullet trains in japanWeb5 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. how fast are cats