Ordering Graphs with Maximum Degree \(3\) by Their Indices

Kexiang Xu1,2, Baogang Xu1
1School of Math. & Computer Science Nanjing Normal University, Nanjing, 210097
2College of Science Nanjing University of Aeronautics & Astronautics Nanjing, 210016

Abstract

We consider the connected graphs with a unique vertex of maximum degree \(3\). Two subfamilies of such graphs are characterized and ordered completely by their indices. Moreover, a conjecture about the complete ordering of all graphs in this set is proposed.