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.

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“…Lemma 2.4. [5] Let G be a graph of order n with m ≥ 1 edges. Let q 1 ≤ q 2 • • • ≤ q n denote the signless Laplacian eigenvalues of G. Then…”

“…Recently, the Laplacian-energy-like invariants are explored for some graph operations on regular and semi-regular graphs in [23] and [26]. New bounds on the Laplacian-energy-like invariant and incidence energy of the line graph, subdivision graph and total graph of regular graphs have been obtained in [3] and [5]. Motivated by such results, in this paper, we give the bounds on the Laplacian-energy-like invariant and incidence energy for some important graph operations, namely the corona and edge corona of two graphs.…”

Bounds on some energy-like invariants of corona and edge corona of graphs

“…Lemma 2.4. [5] Let G be a graph of order n with m ≥ 1 edges. Let q 1 ≤ q 2 • • • ≤ q n denote the signless Laplacian eigenvalues of G. Then…”

“…Recently, the Laplacian-energy-like invariants are explored for some graph operations on regular and semi-regular graphs in [23] and [26]. New bounds on the Laplacian-energy-like invariant and incidence energy of the line graph, subdivision graph and total graph of regular graphs have been obtained in [3] and [5]. Motivated by such results, in this paper, we give the bounds on the Laplacian-energy-like invariant and incidence energy for some important graph operations, namely the corona and edge corona of two graphs.…”