A Sharp Upper Bound on the Least Signless Laplacian Eigenvalue Using Domination Number
β Scribed by Chang-Xiang He, Min Zhou
- Book ID
- 120788866
- Publisher
- Springer Japan
- Year
- 2013
- Tongue
- English
- Weight
- 261 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
Let G be a connected graph of order n. The algebraic connectivity of G is the second smallest eigenvalue of the Laplacian matrix of G. A dominating set in G is a vertex subset S such that each vertex of G that is not in S is adjacent to a vertex in S. The least cardinality of a dominating set is the
We prove that the minimum value of the least eigenvalue of the signless Laplacian of a connected nonbipartite graph with a prescribed number of vertices is attained solely in the unicyclic graph obtained from a triangle by attaching a path at one of its endvertices.
We consider weighted graphs, where the edge weights are positive definite matrices. The Laplacian of the graph is defined in the usual way. We obtain an upper bound on the largest eigenvalue of the Laplacian and characterize graphs for which the bound is attained. The classical bound of Anderson and