3,503 research outputs found
The trace of uniform hypergraphs with application to Estrada index
In this paper we investigate the traces of the adjacency tensor of
hypergraphs (simply called the traces of hypergraphs). We give new expressions
for the traces of hypertrees and linear unicyclic hypergraphs by the weight
function assigned to their connected sub-hypergraphs, and provide some
perturbation results for the traces of a hypergraph with cut vertices. As
applications we determine the unique hypertree with maximum Estrada index among
all hypertrees with fixed number of edges and perfect matchings, and the unique
unicyclic hypergraph with maximum Estrada index among all unicyclic hypergraph
with fixed number of edges and girth
High-ordered spectral characterization of unicyclic graphs
In this paper we will apply the tensor and its traces to investigate the
spectral characterization of unicyclic graphs. Let be a graph and be
the -th power (hypergraph) of . The spectrum of is referring to its
adjacency matrix, and the spectrum of is referring to its adjacency
tensor. The graph is called determined by high-ordered spectra (DHS for
short) if, whenever is a graph such that is cospectral with for
all , then is isomorphic to . In this paper we first give formulas
for the traces of the power of unicyclic graphs, and then provide some
high-ordered cospectral invariants of unicyclic graphs. We prove that a class
of unicyclic graphs with cospectral mates is DHS, and give two examples of
infinitely many pairs of cospectral unicyclic graphs but with different
high-ordered spectra
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