On Relation Between Kirchhoff Index, Laplacian-Energy-Like Invariant and Laplacian Energy of Graphs

作者：Das, Kinkar Ch^*; Xu, Kexiang

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2016, 39(S1): S59-S75.

DOI：10.1007/s40840-015-0280-4

• Graph
• Laplacian spectrum (of graph)
• Spanning tree
• Kirchhoff index
• Laplacian-energy-like invariant
• Laplacian energy

Let G = (V, E) be a simple graph of order n with m edges and Laplacian eigenvalues mu(1) >= mu(2) >= ... >= mu(n-1) >= mu(n) = 0. The Kirchhoff index and the Laplacian-energy-like invariant of G are defined as
Kf(G) = n Sigma(n-1)(k=1) 1/mu(k) and LEL(G) = Sigma(n-1)(k=1) root mu(k),
respectively. The Laplacian energy of the graph G is defined as
LE(G) = Sigma(n)(i=1) vertical bar mu(i) - 2m/n vertical bar.
In this paper, we present an upper bound on Kf of graphs. Also, we obtain some relations between Kf, LEL and first Zagreb index of G. Finally, we give a relation between LEL and LE of G.

• 出版日期2016-6
• 单位南京航空航天大学