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Browsing Research, Scholarship, and Creative Works by Author "Ahmadi, Bahman"

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    Minimum number of distinct eigenvalues of graphs
    (International Linear Algebra Society, 2013-09) Ahmadi, Bahman; Alinaghipour, Fatemeh; Cavers, Michael; Fallat, Shaun; Meagher, Karen; Nasserasr, Shahla
    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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    On Some Graphs Associated with Permutations
    (University of Regina Graduate Students' Association, 2011-04-02) Ahmadi, Bahman
    A permutation on the set X = {1, 2, ... , n} is a bijective function from X to itself. The set of all permutations on X is called the symmetric group and is denoted by Sym(n). An m-cyclic permutation is a permutation which moves m elements of X "cycle-wise" and does not move the other elements. For any 2<=m<=n define the graph "Gamma(n,m)" to be the graph whose vertices are all the elements of Sym(n) and two vertices are adjacent if one of them is equal to the composition of the other one with an m-cyclic permutation. In this talk we study the maximum independent sets of these graphs.