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Chromatic Curling Number of Certain Derived Graphs

Susanth Chandoor, Sudev Naduvath, Sunny Joseph Kalayathankal


The curling number of a graph G is dened as the number of times an element in the degree sequence of G appears the maximum number of times. Graph colouring is an assignment of colours, labels or weights to the vertices or edges of a graph. A colouring C of colours c1, c2,..., cl is said to be a minimum parameter colouring if C consists of minimum number of colours with smallest subscripts. In this paper, we study the chromatic colouring version of curling number of certain derived graphs, with respect to their minimum parameter colourings.


Graph colouring; curling number; compound curling number; chro- matic curling number; chromatic compound curling number.

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J.A. Bondy and U.S.R. Murty, Graph theory, (Springer, New York, 2008).

G. Chartrand and P. Zhang, Chromatic graph theory, (CRC Press, Boca Raton,


B. Chan, J. P. Linderman, N. J. A. Sloane, A. R. Wilks, On curling numbers

of integer sequences, J. Integer Seq., 16(2013), Article-13.4.3, 1-31.

B. Chan, N. J. A. Sloane, The curling number conjecture, Preprint,

arXiv:0912.2382v5 [math.CO].

K.P. Chithra, E.A. Shiny and N.K. Sudev, On colouring parameters of certain

cycle related graphs, Contemp. Stud. Discrete Math., 1(1)(2017), 1{10.

K.P. Chithra, N.K. Sudev, S. Satheesh, K.A. Germina and J. Kok, On cer-

tain colouring parameters of Mycielski graphs of some graphs, Discrete Math.

Algorithm Appl., (2017), to appear.

F. Fornasiero and S. Naduvath, On J-colourability of certain derived graph

classes, communicated.

F. Harary, Graph theory, (Narosa Publ., New Delhi, 2001).

T.R. Jensen and B. Toft, Graph colouring problems, (John Wiley & Sons, 1995).

M. Kubale, Graph colourings, (American Mathematical Society, 2004).

J. Kok, N.K. Sudev, and U. Mary, On chromatic Zagreb indices of certain

graphs, Discrete Math. Algorithm. Appl., 09(1)(2017), 1750014:1-14, DOI:


J. Kok, N. K. Sudev, K. P. Chithra, On curling number of certain graphs,

Southeast Asian Bull. Math., (2017), in press.

W. Lin, J. Wu, P. C. B. Lam, G. Gu, Several parameters of gen-

eralized Mycielskians, Discrete Appl. Math., 154(8)(2006), 1173-1182,


W. Meyer, Chromatic colouring, Amer. Math. Monthly, 80(1973), 920{922.

N.K. Sudev, K.P. Chithra, S. Satheesh and J. Kok, On certain parameters

of equitable colouring of graphs, Discrete Math. Algorithm Appl., 9(4)(2017),

{11., DOI: 10.1142/S1793830917500549.

N.K. Sudev, Some new results on equitable coloring parameters of graphs,


N.K. Sudev, On the curling number of the Mycielskian of certain graphs, J.

Combin. Math. Combin. Comput, to appear.

N. Sudev, C. Susanth, K. Chithra, J. Kok and S.J. Kalayathankal, Some new

results on the curling number of graphs, J. Combin. Math. Combin. Comput,

to appear.

C. Susanth, S.J. Kalayathankal, N.K. Sudev, K.P. Chithra and J. Kok, Curling

number of certain graph classes, J. Combin. Math. Combin. Comput, to appear.

C. Susanth, S.J. Kalayathankal, N.K. Sudev, K.P. Chithra and J. Kok, Curling

number of certain graph powers, preprint, arXiv:1509.00220 [math.GM]

D.B. West, Introduction to graph theory, (Pearson Education Inc., Delhi 2001).


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