## Abstract Chartrand and Stewart have shown that the line graph of an __n__βconnected graph is itself __n__βconnected. This paper shows that for every pair of integers __m__ > __n__ > 1 there is a graph of point connectivity __n__ whose line graph has point connectivity __m__. The corresponding qu
Graphs with prescribed local connectivities
β Scribed by Donald W. Vanderjagt
- Publisher
- Elsevier Science
- Year
- 1974
- Tongue
- English
- Weight
- 537 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The eccentricity e(v) of a vertex v in a connected graph G is the distance between v and a vertex furthest from v in G. The center C(G) of G is the subgraph induced by those vertices of G having minimum eccentricity; the periphery P(G) is the subgraph induced by those vertices of G having maximum ec
d 2,n 2 ) is a bipartite graphical sequence, if there is a bipartite graph G with degrees {D 1 , D 2 } (i.e., G has two independent vertex sets In other words, {D 1 , D 2 } is a bipartite graphical sequence if and only if there is an n 1 1 n 2 matrix of 0's and 1's having d 1j 1 1's in row j 1 and
The local connectivity ΞΊ(u, v) of two vertices u and v in a graph G is the maximum number of internally disjoint u-v paths in G, and the connectivity of G is defined as } for all pairs u and v of vertices in G. Let Ξ΄(G) be the minimum degree of G. We call a graph G maximally connected when ΞΊ(G) = Ξ΄