AUTHOR=Lu Hongyan , Zhu Zhongxun TITLE=On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs JOURNAL=Frontiers in Physics VOLUME=8 YEAR=2020 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00208 DOI=10.3389/fphy.2020.00208 ISSN=2296-424X ABSTRACT=

With the wide application of graph theory in circuit layout, signal flow chart and power system, more and more attention has been paid to the network topology analysis method of graph theory. In this paper, we construct a graph transformation which can reflect the monotonicity of coefficients and reduce the number of graphs. A sharp lower bound for incidence energy in the tricyclic graphs is given and all the extremal structures are characterized. The most interesting things that we find two different classes tricyclic graphs have the same signless Laplacian characteristic polynomials and one of the extremal graphs beyond all expectations.