The least eigenvalue of unicyclic graphs with vertices and pendant vertices
โ Scribed by Ruifang Liu; Mingqing Zhai; Jinlong Shu
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 275 KB
- Volume
- 431
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The energy of a graph G, denoted by E(G), is defined to be the sum of absolute values of all eigenvalues of the adjacency matrix of G. Let G(n, l, p) denote the set of all unicyclic graphs on n vertices with girth and pendent vertices being l ( 3) and p ( 1), respectively. More recently, one of the
The generating function for labelled graphs in which each vertex has degree at least three is obtained by the Principle of Inclusion and Exclusion. Asymptotic and explicit values for the coefficients are calculated in the connected case. The results are extended to bipartite graphs.
This note presents a solution to the following problem posed by Chen, Schelp, and Soltรฉs: find a simple graph with the least number of vertices for which only the degrees of the vertices that appear an odd number of times are given.