Key Generation in Cryptography Using Radio Path Coloring
Dhanyashree, K. N. Meera, Said Broumi · IEEE Access · 2024
AnL(p1,p2,p3,...,pm)-labeling of a graphGis an assignment of positive integers to the vertices ofGsuch that the difference in the labels assigned to the vertices at distanceishould be at leastpi. The particular case ofp1=d,p2=d-1,p3=d-2,...,pd= 1 wheredis the diameter of the graph, was known as the radio labeling ofG. The minimum value of the maximum integer used in any feasible radio labeling ofGwas called as radio number ofGdenoted byrn(G). The idea of radio path coloring was conceived to ensure secure communication in networks. If there exists a path between each pair of vertices, such that, the labeling in that path is anL(p1,p1-1,p1-2,..., 1)-labeling, then such a labeling was called anL(p1,p1-1,p1-2,..., 1)-path coloring or a radio path coloring ofG. The minimum value of the largest label used in such a coloring was called as the radio path connection number. Earlier researchers have studied the case ofp1= 2 for different classes of graphs. We focus on the more general case ofp1≥ 3 and obtain an upper bound on the radio connection numberkp1c(G), of any semi-Hamiltonian graphG. An algorithm to obtain the radio path coloring of a Semi-Hamiltonian graphGis also discussed here and the same is used to generate keys for secure communication in cryptography.