Elementary components of essentially disconnected polyomino graphs

Wei, Shouliu; Ke, Xiaoling

doi:10.1007/s10910-009-9589-2

Cited by 6 publications

(3 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A face f of G is said to be a boundary face if the boundaries of f and ∂(G) have a vertex in common. A polyomino graph P with forbidden edges can be decomposed into some elementary components [23]. A polynomial time algorithm to accomplish this decomposition.…”

Section: Maximum Forcing Numbermentioning

confidence: 99%

“…In general, perfect matching existence [28], elementary components [11,23], matching forcing number [17] and maximal resonance [14] of polyomino graphs have been investigated. In addition, polyomino graphs are also models of many interesting combinatorial subjects, such as hypergraphs [2], domination problem [5,6], rook polynomials [16], etc.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A maximum resonant set of polyomino graphs

Zhang¹,

Zhou²

2016

Discuss. Math. Graph Theory

View full text Add to dashboard Cite

A polyomino graph H is a connected finite subgraph of the infinite plane grid such that each finite face is surrounded by a regular square of side length one and each edge belongs to at least one square. In this paper, we show that if K is a maximum resonant set of H, then H − K has a unique perfect matching. We further prove that the maximum forcing number of a polyomino graph is equal to its Clar number. Based on this result, we have that the maximum forcing number of a polyomino graph can be computed in polynomial time. We also show that if K is a maximal alternating set of H, then H − K has a unique perfect matching.

show abstract

Section: Maximum Forcing Numbermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A maximum resonant set of polyomino graphs

Zhang¹,

Zhou²

2016

Discuss. Math. Graph Theory

View full text Add to dashboard Cite

show abstract

“…Considerable research in statistical physics and structural chemistry has been devoted to polyomino graphs [4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Extremal Matching Energy of Random Polyomino Chains

Lü

Zhang

2017

Entropy

View full text Add to dashboard Cite

Polyomino graphs is one of the research objectives in statistical physics and in modeling problems of surface chemistry. A random polyomino chain is a subgraph of a polyomino graph. The matching energy is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. In this paper, we characterize the graphs with the extremal matching energy among all random polyomino chains of a polyomino graph by the probability method.

show abstract

The structure character of essentially disconnected polyomino graphs

Zhifang

Rongsi

2010

J Math Chem

View full text Add to dashboard Cite

Elementary components of essentially disconnected polyomino graphs

Cited by 6 publications

References 13 publications

A maximum resonant set of polyomino graphs

A maximum resonant set of polyomino graphs

Extremal Matching Energy of Random Polyomino Chains

The structure character of essentially disconnected polyomino graphs

Contact Info

Product

Resources

About