On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number

Abstract

Let φ(L(G))=det (xI−L(G))=∑k=0n(−1)kck(G)xn−k$\phi (L(G)) = \det (xI - L(G)) = \sum\nolimits_{k = 0}^n {( - 1)^k c_k (G)x^{n - k} } $ be the Laplacian characteristic polynomial of G. In this paper, we characterize the minimal graphs with the minimum Laplacian coefficients in 𝒢n,n+2(i) (the set of all tricyclic graphs with fixed order n and matching number i). Furthermore, the graphs with the minimal Laplacian-like energy, which is the sum of square roots of all roots on ϕ(L(G)), is also determined in 𝒢n,n+2(i).

Keywords

• laplacian characteristic polynomial
• laplacian-like energy
• tricyclic graph
• 05c12
• 05c50