- Tytuł:
- Characterizations of the Family of All Generalized Line Graphs—Finite and Infinite—and Classification of the Family of All Graphs Whose Least Eigenvalues ≥ −2
- Autorzy:
- Vijayakumar, Gurusamy Rengasamy
- Powiązania:
- https://bibliotekanauki.pl/articles/29551714.pdf
- Data publikacji:
- 2013-09-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
generalized line graph
enhanced line graph
representation of a graph
extended line graph
least eigenvalue of a graph - Opis:
- The infimum of the least eigenvalues of all finite induced subgraphs of an infinite graph is defined to be its least eigenvalue. In [P.J. Cameron, J.M. Goethals, J.J. Seidel and E.E. Shult, Line graphs, root systems, and elliptic geometry, J. Algebra 43 (1976) 305-327], the class of all finite graphs whose least eigenvalues ≥ −2 has been classified: (1) If a (finite) graph is connected and its least eigenvalue is at least −2, then either it is a generalized line graph or it is represented by the root system E8. In [A. Torgašev, A note on infinite generalized line graphs, in: Proceedings of the Fourth Yugoslav Seminar on Graph Theory, Novi Sad, 1983 (Univ. Novi Sad, 1984) 291- 297], it has been found that (2) any countably infinite connected graph with least eigenvalue ≥ −2 is a generalized line graph. In this article, the family of all generalized line graphs-countable and uncountable-is described algebraically and characterized structurally and an extension of (1) which subsumes (2) is derived.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2013, 33, 4; 637-648
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł