### On the Normalized Laplacian Spectrum of Some Graphs

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**Authors:**R. P. VARGHESE AND D. SUSHA

**DOI:**10.46793/KgJMat2003.431V

**Abstract:**

In this paper we determine the normalized Laplacian spectrum of duplication vertex join of two graphs, duplication graph, splitting graph and double graph of a regular graph. Here we investigate some graph invariants like the normalized Laplacian energy, Kemeny’s constant and number of spanning tree of these graphs.

**Keywords:**

Normalized Laplacian spectrum, normalized Laplacian energy, Kemeny’s constant, spanning tree.

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