Spectral Integral Variations of Degree Maximal Graphs |
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Authors: | Fan Yizheng |
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Institution: |
a Department of Mathematics, Anhui University, Hefei, Anhui 230039, P.R. China. |
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Abstract: | The concept of the spectral integral variation was introduced by Fan Fan Yizheng (2002). On spectral integral variations of graphs. Linear and Multilinear Algebra , 50 , 133-142] to study the general graphs with all changed eigenvalues moving up by integers when an edge is added. Here we consider the spectral integral variations of maximal graphs G , and successfully give an equivalent condition for the spectral integral variation of G occurring in two places by adding an edge e . We also characterize whether the graph G + e is maximal so that an explicit interpretation of the above condition is obtained, where G + e denotes the graph obtained from G by adding an edge e . |
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Keywords: | Laplacian Matrix Laplacian Integral Spectral Integral Variation Degree Maximal Graph |
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