Abstract
Let G be a simple graph of order n. For , the -matrix of G is defined as , where and are the adjacency matrix and the diagonal degree matrix of G, respectively. The eigenvalues of the -matrix of G are called the -eigenvalues of G. In this paper, we first study the properties on -eigenvalues, i.e. how the -eigenvalues behave under some kinds of graph transformations including vertex deletion, vertex contraction, edge deletion and edge subdivision. Moreover, we also present the relationships between the -eigenvalues of G and its k-domination number, independence number, chromatic number and circumference, respectively.
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