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: Gurusamy Rengasamy Vijayakumar
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

generalized line graph; enhanced line graph; representation of a graph; extended line graph; least eigenvalue of a graph

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 4
• Strony: 637-648

Daty

wydano

2013-09-01

online

2013-10-15

Twórcy

autor

Gurusamy Rengasamy Vijayakumar

• School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road, Colaba, Mumbai 400 005, India

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1691