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Wiener index of generalized stars and their quadratic line graphs

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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

1 Discussiones Mathematicae Graph Theory

1 Dobrynin A.

1 Mel'nikov L.

1 2006

Wyniki wyszukiwania

Wiener index of generalized stars and their quadratic line graphs