# Wiener index of generalized stars and their quadratic line graphs

Andrey A. Dobrynin; Leonid S. Mel'nikov

Discussiones Mathematicae Graph Theory (2006)

- Volume: 26, Issue: 1, page 161-175
- ISSN: 2083-5892

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topAndrey A. Dobrynin, and Leonid S. Mel'nikov. "Wiener index of generalized stars and their quadratic line graphs." Discussiones Mathematicae Graph Theory 26.1 (2006): 161-175. <http://eudml.org/doc/270582>.

@article{AndreyA2006,

abstract = {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.},

author = {Andrey A. Dobrynin, Leonid S. Mel'nikov},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {distance in a graph; Wiener index; star; iterated line graph; line graph},

language = {eng},

number = {1},

pages = {161-175},

title = {Wiener index of generalized stars and their quadratic line graphs},

url = {http://eudml.org/doc/270582},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Andrey A. Dobrynin

AU - Leonid S. Mel'nikov

TI - Wiener index of generalized stars and their quadratic line graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2006

VL - 26

IS - 1

SP - 161

EP - 175

AB - 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.

LA - eng

KW - distance in a graph; Wiener index; star; iterated line graph; line graph

UR - http://eudml.org/doc/270582

ER -

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