On powers and centers of chordal graphs

A graph is chordal if every cycle of length strictly greater than three has a chord. A necessary and sufficient condition is given for all powers of a chordal graph to be chordal. In addition, it is shown that for connected chordal graphs the center (the set of all vertices with minimum eccentricity) always induces a connected subgraph. A relationship between the radius and diameter of chordal graphs is also established.