A note on the order graph of a group

 The order graph of a group G, denoted by \Gamma^*(G), is a graph whose vertices are subgroups of G and two distinct vertices H and K are adjacent if and only if |H|\big{|}|K| or |K|\big{|}|H|. In this paper, we study the connectivity and diameter of this  graph. Also we give a relation between the order graph and prime  graph of a group.

کلیدواژه ها:

Connected graph ، Frobenius group ، Order graph ، Prime graph