Topic
Hexagonal number
About: Hexagonal number is a research topic. Over the lifetime, 33 publications have been published within this topic receiving 314 citations.
Papers
TL;DR: In this paper, extremal properties of the linear chain of hexagonal chains with hexagons with hexagonal hexagons have been investigated, and the extremality of the chain with respect to Z, σ and σ has been shown.
Abstract: Some extremal properties of the linear chainLh ofh hexagons are pointed out. In the class of all hexagonal chains withh hexagons,Lh has minimumK,Z andx1 values, as well as maximum W and σ values;K = number of perfect matchings,Z = number of independent edge sets (Hosoya index),x1 = largest graph eigenvalue,W = Wiener index, σ= number of independent vertex sets (Merrifield-Simmons index). The extremality ofLh with respect toZ, σ andx1 is demonstrated here for the first time.
78 citations
TL;DR: In this article, a grammar for generating hexagonal arrays on a triangular grid is presented, and a new kind of catenation, called arrowhead catenations, is defined so that the hexagonal shape is maintained in every generation.
39 citations
Proceedings Article•
1 Jan 2007
TL;DR: It is shown that Hamilton circuit in hexagonal grid graphs is NP-complete.
Abstract: We look at a variant of the Hamilton circuit problem, where the input is restricted to hexagonal grid graphs. A hexagonal grid graph has a vertex set that is a subset of the grid points of a regular hexagonal tiling of the plane and edges corresponding to hexagon sides. We show that Hamilton circuit in hexagonal grid graphs is NP-complete.
21 citations
21 citations
1 Jan 2015
TL;DR: In this article, the Clar number of a peri-condensed hexagonal system with a perfect matching was shown to be at least jKj + 2, where k is the number of disjoint M-alternating hexagons of the system.
Abstract: Let H be a hexagonal system with a perfect matching. Xu et al. discovered that the maximum forcing number of H equals its Clar number. In this article we obtain a result: for any resonant set K of a peri-condensed hexagonal system H consisting of disjoint hexagons not meeting the boundary of H, if the subgraph obtained from H by deleting K and the boundary of H has a perfect matching or is empty, then the Clar number of H is at least jKj + 2. This fact improves the previous corresponding result due to Zheng and Chen. Based on the result, we prove that for each perfect matching M of H with the maximum forcing number, there exists a Clar set consisting of disjoint M-alternating hexagons of H.
19 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2017 | 3 |
| 2016 | 1 |
| 2015 | 3 |
| 2014 | 1 |
| 2013 | 2 |