Some improved bounds on two energy-like invariants of some derived graphs

Abstract

Given a simple graph G, its Laplacian-energy-like invariant LEL(G) and incidence energy IE(G) are the sum of square root of its all Laplacian eigenvalues and signless Laplacian eigenvalues, respectively. This paper obtains some improved bounds on LEL and IE of the 𝓡-graph and 𝓠-graph for a regular graph. Theoretical analysis indicates that these results improve some known results. In addition, some new lower bounds on LEL and IE of the line graph of a semiregular graph are also given.

Keywords

• spectrum
• incidence energy
• 𝓡-graph
• 𝓠-graph
• laplacian-energy-like invariant
• 05c05
• 05c12
• 05c50