Consider L^i(T) is a graph with "even triangle"(triangle with even degrees of vertices) subgraph. Edges of even triangle produce new even triangle in L^(i+1)(T). And if there is an odd degree vertex adjacent to parent triangle, there would be another one adjacent to child. So, irregular subgraph remains.

## No

Consider L^i(T) is a graph with "even triangle"(triangle with even degrees of vertices) subgraph. Edges of even triangle produce new even triangle in L^(i+1)(T). And if there is an odd degree vertex adjacent to parent triangle, there would be another one adjacent to child. So, irregular subgraph remains.