Radio numbers of j-vertex handle semi-complete graphs

Radio labeling is a form of distance labeling of graphs. We explore which positive integers are achievable radio numbers for graphs of order n. Previous results show that all integers in [n, 4n-11] are achieved as the radio numbers of j-vertex handle semi-complete graphs for j = 0, 1, 2. We extend the previous known interval by determining radio numbers for larger values of j. These radio numbers are established by developing theoretical lower bounds based on maximum possible distances between consecutively labeled vertices that meet upper bounds produced through our own radio labeling schemes.