Geodesic
On the spectral radii of quasi-tree graphs and quasi-unicyclic graphs with k pendent vertices
The electronic journal of linear algebra, Tome 20 (2010), pp. 391-405.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A connected graph G = (V, E) is called a quasi-tree graph if there exists a vertex u $0 \in V$ (G) such that G - u 0 is a tree. A connected graph G = (V, E) is called a quasi-unicyclic graph if there exists a vertex u $0 \in V$ (G) such that G - u 0 is a unicyclic graph. Set T (n, k) := G : G is a n -vertex quasi-tree graph with k pendant vertices, and T (n, d 0 , k ) := G : G $\in T$ (n, k) and there is a vertex u $0 \in V$ (G) such that G - u 0 is a tree and d $G(u 0 ) = d 0$ . Similarly, set U (n, k) := G : G is a n-vertex quasi-unicyclic graph with k pendant vertices, and U (n, d 0 , k ) := G : G $\in U$ (n, k) and there is a vertex u $0 \in V$ (G) such that G - u 0 is a unicyclic graph and d $G(u 0 ) = d 0$ . In this paper, the maximal spectral radii of all graphs in the sets T (n, k), T (n, d 0 , k ), U (n, k), and U (n, d 0 , k ), are determined. The corresponding extremal graphs are also characterized.
Classification : 05C50
Keywords: quasi-tree graph, quasi-unicyclic graph, eigenvalues, pendant vertex, spectral radius 
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     author = {Geng, Xianya and Li, Shuchao},
     title = {On the spectral radii of quasi-tree graphs and quasi-unicyclic graphs with k pendent vertices},
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Geng, Xianya; Li, Shuchao. On the spectral radii of quasi-tree graphs and quasi-unicyclic graphs with k pendent vertices. The electronic journal of linear algebra, Tome 20 (2010), pp. 391-405. http://geodesic.mathdoc.fr/item/ELA_2010__20__a24/