Extremal properties of the distance spectral radius of hypergraphs

Abstract

<jats:p>The distance spectral radius of a connected hypergraph is the largest eigenvalue of its distance matrix. The unique hypertrees with minimum distance spectral radii are determined in the class of hypertrees of given diameter, in the class of hypertrees of given matching number, and in the class of non-hyperstar-like hypertrees, respectively. The unique hypergraphs with minimum and second minimum distance spectral radii are determined in the class of unicylic hypergraphs. The unique hypertree with maximum distance spectral radius is determined in the class of $k$-th power hypertrees of given matching number.</jats:p>

The Distance Spectral Radii of Hypercacti

“…Further, they studied other hypertree classes for this problem, such as nonhyperstar-like hypertrees，non-hyper-caterpillars ( [3]). On the hypertree class with fixed invariants, Wang and Zhou [4] characterized the extreme hypertree of given diameter (or given matching number) with minimum DSR. Some further results can be found in literature [5][6][7].…”

“…Let H be a cycle with old length , where ≥ 5. Suppose H  is the hypergraph obtained by identifying three consecutive vertices in H , deleting two common edges which contain(4) two of these three vertices, and adding two new pendent edges at the identified vertex, then If 1 ≇ , where is a cycle of length . We have the following facts:Fact 1.…”