Faculty and Student Publications
Document Type
Article
Publication Date
6-1-2020
Abstract
© 2020 by the authors. Let A(G) be the adjacent matrix and D(G) the diagonal matrix of the degrees of a graph G, respectively. For 0 ≤ α ≤ 1, the Aα-matrix is the general adjacency and signless Laplacian spectral matrix having the form of Aα(G) = αD(G) + (1-α)A(G). Clearly, A0(G) is the adjacent matrix and 2A1/2 is the signless Laplacian matrix. A cactus is a connected graph such that any two of its cycles have at most one common vertex, that is an extension of the tree. The Aα-spectral radius of a cactus graph with n vertices and k cycles is explored. The outcomes obtained in this paper can imply some previous bounds from trees to cacti. In addition, the corresponding extremal graphs are determined. Furthermore, we proposed all eigenvalues of such extremal cacti. Our results extended and enriched previous known results.
Relational Format
journal article
Recommended Citation
Wang, C., Wang, S., Liu, J.-B., & Wei, B. (2020). On the Aα-Spectral Radii of Cactus Graphs. Mathematics, 8(6), 869. https://doi.org/10.3390/math8060869
DOI
10.3390/math8060869
Accessibility Status
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