On problems and conjectures on adjointly equivalent graphs

Abstract: For a graph G, let denote its adjoint polynomial and denote the minimum real root of . Two graphs H and G are said to be adjointly equivalent if . Let and . In this paper, we give a necessary and sufficient condition for two graphs H and G in to be adjointly equivalent, where . We also solve some problems and conjectures proposed by Dong et al. (Discrete Math. 258 (2002) 303–321). [Copyright &y& Elsevier]