Journal of Mathematical Chemistry

, Volume 49, Issue 2, pp 489–506 | Cite as

The structure character of essentially disconnected polyomino graphs

  • Liu Zhifang
  • C. Rongsi
Original Paper


This paper deals with the structure of essentially disconnected polyomino graphs. It is proved that for an essentially disconnected polyomino graph, the normal components induced digraph is acyclic and connected. The lower bond for the number of normal components of an essentially disconnected polyomino graph is investigated. Moreover, the essentially disconnected polyomino graphs with two or three normal components are classified and constructed.


Construction Polyomino graph Matching Fixed bond Essentially disconnected Normal 


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  1. 1.
    Berge C., Chen C.C., Chvatal V., Seow C.S.: Combinatorial properties of polymonoes. Combinatorics 1, 217–224 (1981)CrossRefGoogle Scholar
  2. 2.
    Cockayne E.J.: Chessboard domination problem. Discret. Math. 86, 13–20 (1990)CrossRefGoogle Scholar
  3. 3.
    Harary F., Mezey P.G.: Cell-shedding transformations, equivalence relations, and similarity measures for square-cell configurations. Int. Quant. Chem. 62, 353–361 (1997)CrossRefGoogle Scholar
  4. 4.
    Grinstead C.M., Hahne B., Van Stone D.: On the queen domination problem. Discret. Math 86, 21–26 (1990)CrossRefGoogle Scholar
  5. 5.
    Motoyama A., Hosoya H.: King and domino polyominals for polyomino graphs. J. Math. Phys. 18, 1485–1490 (1997)CrossRefGoogle Scholar
  6. 6.
    Hosoya H.: On some counting polyominals in chemistry. Discret. Appl. Math. 19, 239–257 (1988)CrossRefGoogle Scholar
  7. 7.
    Wei S.L., Ke X.L.: Elementary components of essentially disconnected polyomino graphs. J. Math. Chem. 47, 496–504 (2010)CrossRefGoogle Scholar
  8. 8.
    Zhang H.P., Zhang F.J.: Perfect matchings of polyomino graphs. Gr. Comb. 13, 295–304 (1997)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Information TechnologyFujian Jiangxia CollegeFuzhouPeople’s Republic of China
  2. 2.Center for Discrete Mathematics and Theoretical Computer ScienceFuzhou UniversityFuzhouPeople’s Republic of China

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