Connected graphs of fixed order and size with maximal index: structural considerations

Abstract

The largest eigenvalue, or index, of simple graphs is extensively studied in literature. Usually, the authors consider the graphs from some fixed class and identify within it those graphs with maximal (or minimal) index. So far maximal graphs with fixed order, or with fixed size, are identified, but not maximal connected graphs with fixed order and size. In this paper we add some new observations related to the structure of the latter graphs.