Non-commuting graphs of some finite P-groups - Sarmin, Nor Haniza
Let G be a metacyclic p-group and Z(G) be its center. The non-commuting graph ΓG of a metacyclic p-group G is defined as the graph whose vertex set is G-Z(G) and two distinct vertices x and y are connected by an edge if and only if [x, y] ≠ 1. It is proved that the clique number and chromatic number of graph ΓG associated with the metacyclic p-group G are identical.