ArticleOriginal scientific text
Title
p-Wiener intervals and p-Wiener free intervals
Authors 1, 2
Affiliations
- Center for Research and Post Graduate Studies in Mathematics, Ayya Nadar Janaki Ammal College, Sivakasi - 626 124,Tamil Nadu, India
- Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215,Tamil Nadu, India
Abstract
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.
Keywords
Wiener index of a graph, Wiener graphical, p-Wiener interval, p-Wiener free interval, hyper-Wiener index of a graph, radius, diameter
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Pages:
121-127
Main language of publication
English
Received
2010-07-08
Accepted
2011-02-15
Published
2012
DOI: 10.7151/dmgt.1590
Exact and natural sciences