In the research of QSAR and QSPR correlations, topological indices such as Randi’c index, Zagreb ABC geometric-arithmetic index have been proposed to analyze bio-compatibility chemical compounds. Chemical graph theory is combination Chemistry Graph theory, this deals with topology mathematical study isomerism development which has applications in QSPR. article, we consider Octahedron networks f...

In this article we prove a generalization of Selberg’s lemma on the existence of torsion free, finite index subgroups of arithmetic groups. Some of the geometric applications are the resolution a conjecture of Nimershiem and answers to questions of Long–Reid and the author.