A positive integer n is said to be Wiener graphical, if there exists a graph G with Wiener index n. In this paper, we prove that any positive integer n(≠ 2,5) is Wiener graphical. For any positive integer p, an interval [a,b] is said to be a p-Wiener interval if for each positive integer n ∈ [a,b] there exists a graph G on p vertices such that W(G) = n. For any positive integer p, an interval [a,b] is said to be p-Wiener free interval (p-hyper-Wiener free interval) if there exist no graph G on p vertices with a ≤ W(G) ≤ b (a ≤ WW(G) ≤ b). In this paper, we determine some p-Wiener intervals and p-Wiener free intervals for some fixed positive integer p.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1590,
author = {Kumarappan Kathiresan and S. Arockiaraj},
title = {p-Wiener intervals and p-Wiener free intervals},
journal = {Discussiones Mathematicae Graph Theory},
volume = {32},
year = {2012},
pages = {121-127},
zbl = {1255.05061},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1590}
}
Kumarappan Kathiresan; S. Arockiaraj. p-Wiener intervals and p-Wiener free intervals. Discussiones Mathematicae Graph Theory, Tome 32 (2012) pp. 121-127. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1590/
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