The existence of 1-factors in line graphs, squares, and total graphs
β Scribed by Gary Chartrand; Albert D. Polimeni; M. James Stewart
- Book ID
- 108046826
- Publisher
- Elsevier Science
- Year
- 1973
- Weight
- 320 KB
- Volume
- 76
- Category
- Article
- ISSN
- 1385-7258
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## It is shown that if H --is a COMecied Stial graph of order 2n then 'Y has at least 4n -4 I-facton with equality if and only if M is the total graph of K1 + (& LJ &).
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 A 1βfactorization is constructed for the line graph of the complete graph __K~n~__ when __n__ is congruent to 0 or 1 modulo 4.
## 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 Ξ», and minimum degree Ξ΄ of __G.__ It is