In this paper, we firstly consider how the normalized Laplacian spectral radius of a non-bipartite graph behaves by several graph operations. As applications of the result, the largest normalized Laplacian spectral radius of non-bipartite unicyclic graphs with fixed order and girth is determined. Moreover, the largest normalized Laplacian spectral radius among non-bipartite unicyclic graphs with fixed girth and order is also determined. The maximizer is the tadpole graph with the same (odd) girth.
|Number of pages||11|
|Journal||Bulletin of the Malaysian Mathematical Sciences Society|
|Publication status||Published - 1 Jun 2016|
Scopus Subject Areas
- Non-bipartite graph
- Normalized Laplacian spectral radius
- Unicyclic graph