It is known that the class of line graphs of linear 3-uniform hypergraphs cannot be characterized by a finite list of forbidden induced subgraphs (R. N.
On the second largest eigenvalue of line graphs
β Scribed by Petrovi?, Miroslav; Mileki?, Bojana
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 169 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper all connected line graphs whose second largest eigenvalue does not exceed 1 are characterized. Besides, all minimal line graphs with second largest eigenvalue greater than 1 are determined.
π SIMILAR VOLUMES
Given two connected graphs G a = (V a , E a ) and G b = (V b , E b ) with three-dimensional structures. Let n a = |V a |, m a = |E a |, n b = |V b |, and m b = |E b |. Let the maxi- mum order of a vertex in G a (G b ) be l a (l b ). Initially this paper offers a method to find a largest common subgr
Roger 'Handsome' West of Scotland Yard is pitted against a ruthless criminal network. They will stop at nothing in their pursuit of bribery, corruption, and theft. Their target now is the Railway system and amongst them is a cold-blooded killer whom West must capture. Against him is an organisation
The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. Akiyama, Exoo, and Harary conjectured for any simple graph G with maximum degree β. The conjecture has been proved to be true for graphs having β =
Let G be a graph and let t Υ 0 be a real number. Then, We discuss how the toughness of (spanning) subgraphs of G and related graphs depends on (G), we give some sufficient degree conditions implying that (G) Υ t, and we study which subdivisions of 2-connected graphs have minimally 2-tough squares.
Colorings of disk graphs arise in the study of the frequency-assignment problem in broadcast networks. Motivated by the observations that the chromatic number of graphs modeling real networks hardly exceeds their clique number, we examine the related properties of the unit disk (UD) graphs and their