Chromatic Zagreb indices for graphical embodiment of colour clusters

Johan Kok, Sudev Naduvath, Muhammad Kamran Jamil

Abstract


For a colour cluster C = (C1, C2, C3, …, C), where Ci is a colour class such that ∣Ci∣ = ri, a positive integer, we investigate two types of simple connected graph structures G1C, G2C which represent graphical embodiments of the colour cluster such that the chromatic numbers χ(G1C) = χ(G2C) = ℓ and $\min\{\varepsilon(G^{C}_1)\}=\min\{\varepsilon(G^{C}_2)\} =\sum\limits_{i=1}^{\ell}r_i-1$, and ɛ(G) is the size of a graph G. In this paper, we also discuss the chromatic Zagreb indices corresponding to G1C, G2C.


Keywords


Graphical embodiments; colour clusters; colour classes; chromatic Zagreb indices.

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References


H. Abdo, S. Brandt and D. Dimitrov, The total irregularity of a graph, Discrete Math. Theor. Computer Sci., 16(1)(2014), 201-206.

M. O. Alberton, The irregularity of a graph, Ars Combin., 46(1997), 219-225.

J. A. Bondy and U. S. R. Murty, Graph Theory with Applications,

Macmillan Press, London, 1976.

G. Chartrand and L. Lesniak, Graphs and Digraphs, CRC Press, (2000).

G. H. Fath-Tabar, Old and new Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem., 65(2011), 79-84.

F. Harary, Graph Theory, New Age International, New Delhi, 2001.

V. C. Harris, On identities involving Fibonacci numbers, The Fibonacci Quarterly, 3(3)(1965), 214-218.

J. Kok, N. K. Sudev and K. P. Chithra, General colouring sums of graphs, Cogent Math., 3(2016), DOI: 10.1080/23311835.2016.1140002.

J. Kok, N. K. Sudev and U. Mary, On Chromatic Zagreb Indices of Certain Graphs, Discrete Math Algorithm Appl., 9(1)(2017), 1-14, DOI: 10.1142/S1793830917500148.

K. Subba Rao, Some properties of Fibonacci numbers, American Mathematical Monthly, 60(1953), 680-684.

N. K. Sudev, K. P. Chithra and J. Kok, Certain chromatic sums of some cycle related graph classes, Discrete Math. Algorithm. Appl., 8(3)(2016), 1-24, DOI: 10.1142/S1793830916500506.

D. B. West, Introduction to Graph Theory, Pearson Education Inc., Delhi, 2001.

D. Zeitlin, On identities for Fibonacci numbers, American Mathematical Monthly, 70(1963), 987-991.




DOI: http://dx.doi.org/10.19184/ijc.2019.3.1.6

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