Jewel, comb and fan graph are lucky and proper lucky
T. V. Sateesh Kumar, S. Meenakshi · AIP conference proceedings · 2022
Lucky graph admits the total of labeling of neighboring nodes of a graph will not be the same, and if a node is isolated, the total is zero. The proper graph is naming different positive number for adjacent nodes. Here we proved that jewel graph Jn, comb graph CBn and fan graph Fn are lucky graph and proper lucky graph. Also we derived their lucky number η(G) and proper lucky number ηp(G) of the above mentioned graph.