Abstract: Let $G$ be a finite and simple graph. A walk $S$ is a segment of $G$ if the endpoints (not necessarily distinct) of $S$ are of degree 1 or at least 3, and each of the rest vertices is of degree 2 in $G$. In this paper, we determine the graphs that maximize the $p$-spectral radius for $p>1$ among trees, unicyclic and bicyclic graphs with given order and number of segments, respectively.

Key words: $p$-spectral radii, Tree, Unicyclic graph, Bicyclic graph, Segment