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    Minimum number of distinct eigenvalues of graphs

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    Date
    2013-09
    Author
    Ahmadi, Bahman
    Alinaghipour, Fatemeh
    Cavers, Michael
    Fallat, Shaun
    Meagher, Karen
    Nasserasr, Shahla
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    URI
    http://hdl.handle.net/10294/5684
    Abstract
    The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven and then applied to deduce further properties of q(G). It is shown that there is a great number of graphs G for which q(G) = 2. For some families of graphs, such as the join of a graph with itself, complete bipartite graphs, and cycles, this minimum value is obtained. Moreover, examples of graphs G are provided to show that adding and deleting edges or vertices can dramatically change the value of q(G). Finally, the set of graphs G with q(G) near the number of vertices is shown to be a subset of known families of graphs with small maximum multiplicity.
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    Contact Us | Send Feedback | Archer Library | University of Regina