A note on 'some physical and chemical indices of clique-inserted lattices'

This paper is to point out that proposition 3.3 and some results from 'Some physical and chemical indices of clique-inserted lattices' (Zhang 2013 J. Stat. Mech. P10004) are incorrect, since the fact that a subdivision graph of r-regular G is a (r, 2)-semigraph and the graphs of proposition did not satisfy the condition of one of lemmas cited therein. Moreover, some counterexamples are presented; a short proof of the corresponding correct theorem is deduced via utilizing the characteristic polynomial of the Laplacian matrix, which corrects the proposition 3.3 and some related results in Zhang [2]. (paper)