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The structure and existence of 2-factors in iterated line graphs

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Ferrara M., Gould R., Hartke S.

Discussiones Mathematicae Graph Theory

2007

tom 27

nr 3

507-526

We prove several results about the structure of 2-factors in iterated line graphs. Specifically, we give degree conditions on G that ensure L²(G) contains a 2-factor with every possible number of cycles, and we give a sufficient condition for the existence of a 2-factor in L²(G) with all cycle lengths specified. We also give a characterization of the graphs G where $L^k(G)$ contains a 2-factor.

Wiener index of generalized stars and their quadratic line graphs

100%

Dobrynin A., Mel'nikov L.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 1

161-175

The Wiener index, W, is the sum of distances between all pairs of vertices in a graph G. The quadratic line graph is defined as L(L(G)), where L(G) is the line graph of G. A generalized star S is a tree consisting of Δ ≥ 3 paths with the unique common endvertex. A relation between the Wiener index of S and of its quadratic graph is presented. It is shown that generalized stars having the property W(S) = W(L(L(S)) exist only for 4 ≤ Δ ≤ 6. Infinite families of generalized stars with this property are constructed.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Dobrynin A.

1 Ferrara M.

1 Gould R.

1 Hartke S.

1 Mel'nikov L.

1 2007

1 2006

Wyniki wyszukiwania

The structure and existence of 2-factors in iterated line graphs

Wiener index of generalized stars and their quadratic line graphs