Eigenvalues of the k‐th power of a graph |
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Authors: | Kinkar Ch Das Ji‐Ming Guo |
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Institution: | 1. Department of Mathematics, Sungkyunkwan University, Suwon, Republic of Korea;2. Department of Mathematics, East China University of Science and Technology, Shanghai, P. 3. R. 4. China |
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Abstract: | The k‐th power of a graph G, denoted by , is a graph with the same set of vertices as G such that two vertices are adjacent in if and only if their distance in G is at most k. In this paper, we give the bounds on the spectral radius of and . The Nordhaus–Gaddum‐type inequality for the spectral radius of the graph is also presented. Moreover, we obtain an upper bound on the energy of the second power of graphs. |
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Keywords: | Graph adjacency matrix spectral radius k‐th power of graph Nordhaus– Gaddum‐type inequality diameter 05C50 |
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