Signless Laplacian index conditions for doubly chorded cycles in graphs with given order

Abstract

In this paper, we show that for a graph of order $n$, where $n\ge 5$, if the signless Laplacian index is larger than or equal to certain value depending on $n$, then the graph contains a doubly chorded cycle, where the chords incident to a common vertex, unless it is two specified graphs.

It contains incomplete parts and uncompleted parts