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Continuous Forcing Spectra of Even Polygonal Chains: 《Acta Mathematicae Applicatae Sinica》2021年第2期337-347,共11页He-ping ZHANG Xiao-yan JIANG; supported by the National Natural Science Foundation of China(Nos.11871256,11371180,11226286)。; Let G be a graph that admits a perfect matching M.A forcing set S for a perfect matching M is a subset of M such that it is contained in no other perfect matchings of G.The cardinality of a forcing set of M with the s...; 关键词：perfect matching forcing number forcing spectrum POLYOMINO even polygonal chain Z-transformation graph

Reconstruction of 2-Convex Polyominoes with Non-Empty Corners: 《Open Journal of Discrete Mathematics》2019年第4期83-109,共27页Khalil Tawbe Salwa Mansour; This paper uses the theoretical material developed in a previous study by the authors in order to reconstruct a subclass of 2-convex polyominoes called where the upper left corner and the lower right corner of the pol...; 关键词：POLYOMINO CONVEX Objects MONOTONE Path

2-Convex Polyominoes: Non-Empty Corners: 《Open Journal of Discrete Mathematics》2019年第2期33-51,共19页Khalil Tawbe Nadine Ghandour Ali Atwi; A polyomino P is called 2-convex if for every two cells there exists a monotone path included in P with at most two changes of direction. This paper studies the geometrical properties of a sub-class of 2-convex polyom...; 关键词：POLYOMINO CONVEX Objects MONOTONE Path

Revisiting a Tiling Hierarchy (II): 《Open Journal of Discrete Mathematics》2018年第2期48-63,共16页Viorel Nitica; In a recent paper, we revisited Golomb’s hierarchy for tiling capabilities of finite sets of polyominoes. We considered the case when only translations are allowed for the tiles. In this classification, for several l...; 关键词：TILING POLYOMINO DEFICIENT Region TILE SET TILING HIERARCHY

Signed Tilings by Ribbon L n-Ominoes, n Odd, via Gröbner Bases被引量：1: 《Open Journal of Discrete Mathematics》2016年第4期297-313,共17页Viorel Nitica; We show that a rectangle can be signed tiled by ribbon L n-ominoes, n odd, if and only if it has a side divisible by n. A consequence of our technique, based on the exhibition of an explicit Gröbner basis, is tha...; 关键词：POLYOMINO Replicating Tile L-Shaped Polyomino Skewed L-Shaped Polyomino Signed Tilings Gröbner Basis Coloring Invariants

On Tilings of Quadrants and Rectangles and Rectangular Pattern被引量：2: 《Open Journal of Discrete Mathematics》2016年第4期351-371,共21页Viorel Nitica; The problem of tiling rectangles by polyominoes generated large interest. A related one is the problem of tiling parallelograms by twisted polyominoes. Both problems are related with tilings of (skewed) quadrants by p...; 关键词：POLYOMINO L-Shaped Polyomino Skewed L-Shaped Polyomino Tiling Rectangles Tiling Quadrants Tiling Parallelograms Rectangular Pattern for Tiling Quadrants/Rectangles

Signed Tilings by Ribbon L n-Ominoes, n Even, via Gröbner Bases被引量：1: 《Open Journal of Discrete Mathematics》2016年第3期185-206,共22页Kenneth Gill Viorel Nitica; Let T_nbe the set of ribbon L-shaped n-ominoes for some n≥4 even, and let T⁺_n be T_n with an extra 2 x 2 square. We investigate signed tilings of rectangles by T_n...; 关键词：POLYOMINO Replicating Tile L-Shaped Polyomino Skewed L-Shaped Polyomino Signed Tilings Gröbner Basis Tiling Rectangles Coloring Invariants

The Multiplicative Zagreb Indices of Nanostructures and Chains: 《Open Journal of Discrete Mathematics》2016年第2期82-88,共7页Wei Gao Mohammad Reza Farahani M. R. Rajesh Kanna; In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemic...; 关键词：Molecular Graph The First Multiplicative Zagreb Index The Second Multiplicative Zagreb Index NANOTUBE Nanostar Polyomino Chain

Every Tiling of the First Quadrant by Ribbon <i>L n</i>-Ominoes Follows the Rectangular Pattern: 《Open Journal of Discrete Mathematics》2015年第2期11-25,共15页Viorel Nitica; Let and let be the set of four ribbon L-shaped n-ominoes. We study tiling problems for regions in a square lattice by . Our main result shows a remarkable property of this set of tiles: any tiling of the first quadran...; 关键词：POLYOMINO Replicating Tile L-Shaped POLYOMINO Skewed L-Shaped POLYOMINO Local Move Property TILING Rectangles RECTANGULAR PATTERN TILING First QUADRANT

RELATION BETWEEN WIENER NUMBERS OF QUASI-HEXAGONAL CHAINS AND QUASI-POLYOMINO CHAINS: 《Journal of Systems Science & Complexity》2010年第4期873-882,共10页Mingfang XIE Fuji ZHANG; supported by the Natural Science Foundation of China under Grant No. 10371102; Let Q_n and B_n denote a quasi-polyomino chain with n squares and a quasi-hexagonalchain with n hexagons,respectively.In this paper,the authors establish a relation between the Wienernumbers of Q_n and B_n:W(Q_n)=1/4[...; 关键词：Hexagonal chain polyomino chain quasi-hexagonal chains quasi-polyomino chain Wiener number.

POLYOMINO