Modified chromatic Schultz polynomial of some cycle related graphs. (English) Zbl 1444.05070
Summary: Let \(\mathcal{C}=c_1, c_2,\dots, c_\ell\) be a proper colouring of a connected graph \(G\) with chromatic number \(\ell\). Then, the chromatic Schultz polynomial \(S(G, x)\) of \(G\) is defined as \(S(G, x) =\sum\limits_{v_i,v_j \in V(G)}( \zeta (v_i) + \zeta (v_j))x^{d(u,v)}\), where \(\zeta (v_i) =s\), when the vertex \(v_i\) has the colour \(c_s\) under \(\mathcal{C}\). In this paper, we study the chromatic Schultz polynomials of certain cycle related graph classes.
Keywords:
graph colouring; \( \chi^- \)-colouring; \( \chi^+ \)-colouring; chromatic Schultz polynomial; modified chromatic Schultz polynomialReferences:
| [1] | J.A. Bondy and U.S.R. Murty, “Graph theory”, Springer, New York, 2008. · Zbl 1134.05001 |
| [2] | A. Brandstädt, V.B. Le and J.P. Spinrad, “Graph classes: A survey”, SIAM, Philadelphia, 1999. · Zbl 0919.05001 |
| [3] | G. Chartrand and P. Zhang, “Chromatic graph theory”, CRC Press, Boca Raton, FL, 2009. · Zbl 1169.05001 |
| [4] | J.A. Gallian, A dynamic survey of graph labeling,Electron. J. Combin.,16(6)(2018), 1- 502. |
| [5] | F. Harary, “Graph theory”, Narosa Publishing House, New Delhi, 2001. · Zbl 1020.05033 |
| [6] | T.R. Jensen and B. Toft, “Graph colouring problems”, John Wiley & Sons, New York, 1995. · Zbl 1377.05064 |
| [7] | Johan Kok, N.K. Sudev and K.P. Chithra, Generalised colouring sums of graphs,Cogent Math.,3(2016), 1-11., DOI: 10.1080/23311835.2016.1140002 · Zbl 1426.05046 |
| [8] | J.Kok, N.K. Sudev and U. Mary, On chromatic Zagreb indices of certain graphs,Discrete Math. Algorithm. Appl.,9(1)(2017), 1-11, DOI: 10.1142/S1793830917500148. · Zbl 1358.05107 |
| [9] | M. Kubale, “Graph colorings”, American Math. Soc., Rhodes Island, 2004. · Zbl 1064.05061 |
| [10] | S. Naduvath, Chromatic Schultz polynomial of certain graphs,Discrete Math. Algorithm. Appl., under review. · Zbl 1428.05065 |
| [11] | M.R.Raja, S.Naduvath and C.Dominic, Chromatic Schultz Polynomial of Graphs,Involve, under review. |
| [12] | D.B. West, “Introduction to graph theory”, Prentice Hall of India, New Delhi, 2005. · Zbl 1121.05304 |
| [13] | E.W. Weisstein, “CRC concise encyclopedia of mathematics”, CRC press, Boca Raton, 2011. · Zbl 1079.00009 |
| [14] | Information system on graph classes and their inclusions (ISGCI), 2001-2014,www. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
