L(2, 1) - Labeling on Jahangir Graph
Udayan M. Prajapati, N. B. Patel · 2020
Labeling problems consist of an assignment of non-negative integers to the nodes of a graph such that the adjacent nodes have labels which differ by at least two, and the nodes at distance two must have different labels. A frequency assignment problem was given by W. K. Hale, in order to assign a frequency (non-negative integer) to each TV or radio transmitter, located at various places such that communication does not interfere. Hale introduced the notion of T-coloring of a graph in 1980, to formulate the frequency assignment problem as a graph coloring problem. In 1988, J. Roberts proposed a variation of the frequency assignment problem in which close transmitters must receive frequencies that are at least two apart. As bandwidth is a limited resource, the main target in FAP is to come up with a frequency assignment using a minimum number of frequencies, i.e. one needs to minimize the span of the labeling proposed.