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Perfect 2-Colorings of k-Regular Graphs

Farzaneh Piri|Saeed Mohammadian Semnani
경북대학교 자연과학대학 수학과|2020.06|Kyungpook Mathematical Journal|제60권 제2호|pp. 349-359|DOI 10.5666/KMJ.2020.60.2.349

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키워드

regular graphperfect 2-coloringtoroidal grid graph
주제분류수학

초록

We study perfect 2-colorings of regular graphs. In particular, we consider the 4-regular case. We obtain a characterization of perfect 2-colorings of toroidal grids.

Abstract

We study perfect 2-colorings of regular graphs. In particular, we consider the 4-regular case. We obtain a characterization of perfect 2-colorings of toroidal grids.

참고문헌 (11)

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  3. N. Biggs, "Algebraic graph theory" (1974), Cambridge University press
  4. I. J. Dejter, "Perfect domination in regular grid graphs", Australas. J. Combin, 42, pp.99~114 (2008)
  5. C. Heuberger, "On planarity and colorability of circulant graphs", Discrete Math, 268, pp.153~169 (2003)
  6. D. B. Khoroshilova, "On circular perfect colorings with two colors", Diskretn. Anal. Issled. Oper, 16, pp.80~92 (2009)
  7. M. Knora, "Efficient domination in cubic vertex-transitive graphs", European J. Combin, 33, pp.1755~1764 (2012)
  8. I. Yu. Mogil’nykh, "Perfect 2-Colorings of Johnson Graphs J(6, 3) and J(7, 3)", Lecture Notes in Computer Science, 5228, pp.11~19 (2008), Springer
  9. N. Obradovic, "Efficient domination in circulant graphs with two chord lengths", Inform. Process. Lett, 102, pp.253~258 (2007)
  10. K. V. Vorob’ev, "On perfect 2-colorings of a hypercube", Siberian Electron. Mat. Izv, 7, pp.65~75 (2010)
  11. D. B. West, "Introduction to graph theory", pp.2002

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