Abstract

Let [Formula: see text] be the set of connected unicyclic graphs of order [Formula: see text] and girth [Formula: see text]. Let [Formula: see text] be obtained from a cycle [Formula: see text] (in an anticlockwise direction) by identifying [Formula: see text] with the root of a rooted tree [Formula: see text] of order [Formula: see text] for each [Formula: see text], where [Formula: see text] and [Formula: see text]. In this note, the graph with the minimal least eigenvalue (and the graph with maximal spread) in [Formula: see text] is determined.

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