Johan Kok - Independent Mathematics Researcher, City of Tshwane, South Africa. Joseph Varghese Kureethara - CHRIST (Deemed to be a University), Bangalore, India.
This paper presents the notion of perfect Lucky \(k\)-colouring. Basic conditions for a perfect Lucky \(k\)-colourable graph are presented. Application thereof is then presented by obtaining the Lucky \(4\)-polynomials for all connected graphs \(G\) on six vertices with ten edges. The chromatic number of these connected graphs is \(\chi(G)=3\) or \(4\). For \(k=\max\{\chi(G): 3\) or \(4\}=4\), it is possible to find Lucky \(4\)-polynomials for all graphs on six vertices and ten edges. The methodology improves substantially on the fundamental methodology such that, vertex partitions begin with Lucky partition forms immediately. Finally, further problems for research related to this study are presented.
Johan Kok, Joseph Varghese Kureethara, A note on perfect Lucky \(k\)-colourable graphs, Journal of Mathematics and Computer Science, 21 (2020), no. 3, 192--197
Kok Johan, Kureethara Joseph Varghese, A note on perfect Lucky \(k\)-colourable graphs. J Math Comput SCI-JM. (2020); 21(3):192--197
Kok, Johan, Kureethara, Joseph Varghese. "A note on perfect Lucky \(k\)-colourable graphs." Journal of Mathematics and Computer Science, 21, no. 3 (2020): 192--197
