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On square sum labelings of graphs

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Abstract. Let G = (V,E) be an (n,m)-graph. A graph G is said to admit a square sum labeling, if its vertices can be labeled with distinct non-negative integers so that the values on the edges, obtained as the sum of the labels of their end vertices, are the first m squares. In this paper we show that certain classes of graphs admit square sum labeling and also that certain classes of graphs do not admit square sum labeling.

Abstract

Abstract. Let G = (V,E) be an (n,m)-graph. A graph G is said to admit a square sum labeling, if its vertices can be labeled with distinct non-negative integers so that the values on the edges, obtained as the sum of the labels of their end vertices, are the first m squares. In this paper we show that certain classes of graphs admit square sum labeling and also that certain classes of graphs do not admit square sum labeling.

참고문헌 (6)

  1. D. M. Burton, "Elementary Number Theory" (1990), Brown Publishers
  2. J. A. Gallian, "A Dynamic Survey of Graph labelling", The Electronic Journal of Combinatorics, 17 (2010)
  3. F. Harary, "Graph Theory" (1969), Addison Wesley
  4. S. M. Hegde, "On triangular sum labelings of graphs, In Labelings of Discrete Structures and Applications", pp.109~115 (2008), Narosa Publishing House
  5. S. K. Vaidya, "Some important results on triangular sum graphs", Applied Mathematical Science, 3(36), pp.1763~1772 (2009)
  6. D. B. West, "Introduction to Graph Theory" (2001), Pearson Education

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