Graph equations for line graphs and total graphs
✍ Scribed by Dragǒs M. Cvetković; Slobodan K. Simić
- Publisher
- Elsevier Science
- Year
- 1975
- Tongue
- English
- Weight
- 653 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0012-365X
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## Abstract The concept of the line graph can be generalized as follows. The __k__‐line graph __L__~__k__~(__G__) of a graph __G__ is defined as a graph whose vertices are the complete subgraphs on __k__ vertices in __G.__ Two distinct such complete subgraphs are adjacent in __L__~__k__~(__G__) if
We construct decompositions of L(K,,), M(K,,) and T(K,,) into the minimum number of line-disjoint spanning forests by applying the usual criterion for a graph to be eulerian. This gives a realization of the arboricity of each of these three graphs. ## 1. Preliminaries In this paper a graph is cons
## Abstract Sharp lower bounds for the point connectivity and line connectivity of the line graph __L(G__) and the total graph __T(G__) of a graph __G__ are determined. The lower bounds are expressed in terms of the point connectivity __k__, line connectivity λ, and minimum degree δ of __G.__ It is