Abstract
Recently, Cioabǎ and Gu obtained a relationship between the spectrum of a regular graph and the existence of spanning trees of bounded degree, generalized connectivity and toughness, respectively. In this paper, motivated by the idea of Cioabǎ and Gu, we determine a connection between the (signless Laplacian and Laplacian) eigenvalues of a graph and its structural properties involving the existence of spanning trees with bounded degrees and generalized connectivity, respectively. We also present a connection between the (signless Laplacian and Laplacian) eigenvalues and toughness of a bipartite graph, respectively. Finally, we obtain a lower bound of toughness in a graph in terms of edge connectivity κ′ and maximum degree Δ.
Original language | English |
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Pages (from-to) | 185-196 |
Number of pages | 12 |
Journal | Bulletin of the Iranian Mathematical Society |
Volume | 47 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2021 |
Keywords
- Connectivity
- Eigenvalue
- Spanning k-tree
- Toughness