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Curling number of rooted product of general graphs

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A curling subsequence is a maximal subsequence C of the degree sequence of a simple connected graph G for which the curling number cn(G) corresponds to the curling number of the degree sequence and hence the curling number of the graph G. The curling number of a graph G may be defined as the number of times an element in the degree sequence of G appears the most and compound curling number of G is the product of multiplicities of the degrees of vertices in G. In this paper we establish the bounds for curling number and find Compound curling number of rooted product graph GoH.

Abstract

A curling subsequence is a maximal subsequence C of the degree sequence of a simple connected graph G for which the curling number cn(G) corresponds to the curling number of the degree sequence and hence the curling number of the graph G. The curling number of a graph G may be defined as the number of times an element in the degree sequence of G appears the most and compound curling number of G is the product of multiplicities of the degrees of vertices in G. In this paper we establish the bounds for curling number and find Compound curling number of rooted product graph GoH.

참고문헌 (12)

  1. J. A. Bonday, "Graph theory with applications" (1976), Macmillan Press
  2. B. Chaffin, "On curling numbers of integer sequences", J.Integer Seq, 16 (2013)
  3. Chandoor Susanth, "A Study on the Curling number of graph classes", ~ (2015)
  4. G. Chartrand, "Graphs and digraphs" (2000), CRC Press
  5. J. T. Gross, "Graph theory and its applications" (2006), CRC Press
  6. R. Hammack, "Handbook of product graphs" (2011), CRC Press
  7. F.Harary, "Graph theory" (2001), New Age International
  8. W. Imrich, "Product graphs: Structure and recognition" (2000), Wiley
  9. J. Kok, "On Curling number of certain graphs", Southeast Asian Bull.Math (2017)
  10. Rashmi S B, "Domination number of Rooted product graph PmoCn", Journal of computer and Mathematical Sciences, 7(9), pp.469~471 (2016)
  11. Rashmi S B, "Total Domination number of Rooted product graph PmoCn", International Journal of Advanced Research in Computer science, 8(6) (2017)
  12. Rashmi S B, "Signed domination number of rooted product of a path with cycle graph", International Journal of Mathematical Trends and Techonology, 58(1) (2018)

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