Abstract
Let G be a connected simple graph with order n and Laplacian matrix L(G). The Laplacian-energy-like of G is defined asLEL(G)=∑i=1nλi, where λi is the eigenvalue of L(G) for i=1,…,n. In this paper, with the aid of Ferrers diagrams of threshold graphs, we provide an algebraic combinatorial approach to determine the graphs with minimal Laplacian-energy-like among all connected graphs having n vertices and m edges, showing that the extremal graph is a special threshold graph, named as the quasi-complete graph.
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