The Laplacian energy of diameter 4 trees

Jamshaid Ul Rahman1 School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui230026, China E-mail: [email protected]

Usman Ali2 Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan60000, Pakistan E-mail: [email protected]

Masood Ur Rehman1 School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui230026, China E-mail: [email protected]Correspondence[email protected]
[email protected]

Abstract

Let T_n be the set of trees with n vertices and having diameter 4. We show that four classes in T_n satisfy a conjecture posed by Radenkovi and Gutman [Total π-electron energy and Laplacian energy: how far the analogy goes? J. Serb. Chem. Soc., 72:12:1343–1350, 2007]. The conjecture relates the Laplacian energy of path P_n, tree T_n, and star S_n.

Subject Classification:

05C50

Keywords:

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The Laplacian energy of diameter 4 trees

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