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Zbl 1205.05148
Liu, Zhongzhu
Energy, Laplacian energy and Zagreb index of line graph, middle graph and total graph. (English)
[J] Int. J. Contemp. Math. Sci. 5, No. 17-20, 895-900 (2010). ISSN 1312-7586; ISSN 1314-7544/e

Summary: The energy of a graph $G$ is defined as the sum of the singular values of its adjacency matrix and the Laplacian energy of $G$ is defined as the sum of the distance between Laplacian eigenvalues and average degree of $G$. We report upper bounds for the energy and Laplacian energy of line graph, middle graph and total graph. The bounds for the Laplacian energy are given using the first Zagreb index of the graph.

MSC 2000:: *05C50 Graphs and matrices

Keywords: energy; Laplacian energy; line graph; middle graph; total graph

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