On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs

Abstract

Read online

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.

Keywords

• incidence energy
• extremal graph
• tricyclic graph
• Laplacian matrix
• signless Laplacian coefficients