The Index of Tricyclic Hamiltonian Graphs with $\mathrm{\Delta }(G)=3$

Abstract

If $G$ is a tricyclic Hamiltonian graph of order $n$ with maximum degree $3$, then $G$ has one of two forms, $X(q,r,s,t)$ and $Y(q,r,s,t)$, where $q+r+s+t=n$. We find the graph $G$ with maximal index by first identifying the graphs of each form having maximal index.