A chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. A perfect elimination ordering in a graph is an ordering of the vertices of the graph such that, for each vertex v, v and the neighbors of v that occur after v in the order form a clique. A graph is chordal if and only if it has a perfect elimination ordering.
IsChordal to test whether the lexicographic product of two graphs g1,g2 is a chordal graph. It returned true and provided a perfect elimination sequence
1, 2, ..., 30. However, vertices of
"1:1", "1:2", ..., "10:3", rather than using Arabic numerals. Therefore, it is difficult for me to extract useful information from the perfect elimination sequence.