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Discussiones Mathematicae Graph Theory

2012 | 32 | 1 | 121-127
Tytuł artykułu

p-Wiener intervals and p-Wiener free intervals

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
121-127
Opis fizyczny
Daty
wydano
2012
otrzymano
2010-07-08
poprawiono
2011-02-15
zaakceptowano
2011-02-15
Twórcy
• Center for Research and Post Graduate Studies in Mathematics, Ayya Nadar Janaki Ammal College, Sivakasi - 626 124,Tamil Nadu, India
autor
• Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215,Tamil Nadu, India
Bibliografia
• [1] F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley Reading, 1990).
• [2] P.G. Doyle and J.L. Snell, Random Walks and Electric Networks (Math. Assoc., Washington, 1984).
• [3] R.C. Entringer, D.E. Jackson and D.A. Snyder, Distance in graphs, Czechoslovak Math. J. 26 (101) 1976.
• [4] D. Goldman, S. Istrail, G. Lancia and A. Picolboni, Algorithmic strategies in Combinatorial Chemistry, in: 11th ACM-SIAM Symposium, Discrete Algorithms (2000) 275-284.
• [5] I. Gutman, Y.N. Yeh, S.L. Lee and J.C. Chen, Wiener number of dendrimers, Comm. Math. Chem., 30 (1994) 103-115.
• [6] I. Gutman, Relation between hyper-Wiener and Wiener index, Chem. Phys. Lett. 364 (2002) 352-356, doi: 10.1016/S0009-2614(02)01343-X.
• [7] KM. Kathiresan and S. Arockiaraj, Wiener indices of generalized complementary prisms, Bull. Inst. Combin. Appl. 59 (2010) 31-45.
• [8] S. Klavžar, P. Zigert and I. Gutman, An algorithm for the calculation of the hyper-Wiener index of benzenoid hydrocarbons, Comput. Chem. 24 (2000) 229-233, doi: 10.1016/S0097-8485(99)00062-5.
• [9] Liu Mu-huo and Xuezhong Tan, The first to (k+1)-th smallest Wiener (Hyper -Wiener) indices of connected graphs, Kragujevac J. Math. 32 (2009) 109-115.
• [10] S. Nikolić, N. Trinajstić and Z. Mihalić, The Wiener index: Development and applications, Croat. Chem. Acta. 68 (1995) 105-129.
• [11] H. Wiener, Structural determination of paraffin boiling points, J. Amer. Chem. Soc. 69 (1947) 17-20, doi: 10.1021/ja01193a005.
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Bibliografia
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