The Index of Tricyclic Hamiltonian Graphs with \(\Delta(G) = 3\)

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.