COLORAÇÃO TOTAL NOS GRAFOS DE CAYLEY h_l,p

Abstract

In this work, we present the limits and the basic concepts of vertex coloring of edges and total of a graph. Soon after, we define the total number of vertices, edges and degree of each vertex of the graphs H_l,p, in addition to their lower and upper bounds for coloring, together with methods properly determined throughout the process. Concluding that, for vertex coloring we used the hamiltonian cycle ordering and application of the greedy method having l ≤ χ′(H_l,p) ≤ l(l − 1) + 1, for edge coloring we used the pairing decomposition method having ∆ ≤ χ′(H_l,p) ≤ ∆ + 1 and the total through different methods being ∆ + 1 ≤ χ′′(H_l,p) ≤ ∆ + 2, however, through the vertex coloring method we were able to perform full coloring on the graphs H_l,p.