Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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ODD-EVEN GRACEFUL GRAPHS

  • Sridevi, R. (Department of Mathematics, Sri S.R.N.M. College) ;
  • Navaneethakrishnan, S. (Department of Mathematics, V.O.C.College) ;
  • Nagarajan, A. (Department of Mathematics, V.O.C.College) ;
  • Nagarajan, K. (Department of Mathematics, S.R.N.M. College)
  • 투고 : 2011.06.20
  • 심사 : 2011.12.26
  • 발행 : 2012.09.30
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초록

The Odd-Even graceful labeling of a graph G with $q$ edges means that there is an injection $f:V (G)$ to $\{1,3,5,{\cdots},2q+1\}$ such that, when each edge $uv$ is assigned the label ${\mid}f(u)-f(v){\mid}$, the resulting edge labels are $\{2,4,6,{\cdots},2q\}$. A graph which admits an odd-even graceful labeling is called an odd-even graceful graph. In this paper, we prove that some well known graphs namely $P_n$, $P_n^+$, $K_{1,n}$, $K_{1,2,n}$, $K_{m,n}$, $B_{m,n}$ are Odd-Even graceful.

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참고문헌

  1. R.B.Gnanajothi, Topics in graph Theory, Ph.D.Thesis, Madurai Kamaraj University, 1991.
  2. G.J.Gallian, A Dynamic survey of graph labeling, The electronic journal of combinotorics, 16 (2009), #DS6.
  3. S.W Golomb, How to number a graph in graph Theory and computing, R.C. Read, ed., Academic Press, New York (1972), 23-37.
  4. A. Rosa, On certain valuations of the vertices of a graph, Theory of graphs (International Symposium, Rome), July (1966).
  5. R. Sridevi, S. Navaneethakrishnan and K. Nagarajan, Odd graceful labeling of some special class of graphs, International Journal of Mathematics Research, To appear.

피인용 문헌

  1. Odd-even graceful labeling of planar grid and prism graphs vol.42, pp.4, 2012, https://doi.org/10.1080/02522667.2020.1800787