- Tytuł:
- The inertia of unicyclic graphs and bicyclic graphs
- Autorzy:
- Liu, Ying
- Powiązania:
- https://bibliotekanauki.pl/articles/728942.pdf
- Data publikacji:
- 2013
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
matching number
inertia
nullity
unicyclic graph
bicyclic graph - Opis:
- Let G be a graph with n vertices and ν(G) be the matching number of G. The inertia of a graph G, In(G) = (n₊,n₋,n₀) is an integer triple specifying the numbers of positive, negative and zero eigenvalues of the adjacency matrix A(G), respectively. Let η(G) = n₀ denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is well known that if G is a tree, then η(G) = n - 2ν(G). Guo et al. [Ji-Ming Guo, Weigen Yan and Yeong-Nan Yeh. On the nullity and the matching number of unicyclic graphs, Linear Algebra and its Applications, 431 (2009), 1293-1301.] proved if G is a unicyclic graph, then η(G) equals n - 2ν(G) - 1, n-2ν(G) or n - 2ν(G) + 2. Barrett et al. determined the inertia sets for trees and graphs with cut vertices. In this paper, we give the nullity of bicyclic graphs ₙ⁺⁺. Furthermore, we determine the inertia set in unicyclic graphs and ₙ⁺⁺, respectively.
- Źródło:
-
Discussiones Mathematicae - General Algebra and Applications; 2013, 33, 1; 109-115
1509-9415 - Pojawia się w:
- Discussiones Mathematicae - General Algebra and Applications
- Dostawca treści:
- Biblioteka Nauki
Artykuł