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Peripheral Wiener Index of a Graph | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 5، دوره 2، شماره 1، شهریور 2017، صفحه 43-56 اصل مقاله (481.44 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2017.13596 | ||
| نویسندگان | ||
| Kishori P Narayankar* ؛ Lokesh S B | ||
| Mangalore University | ||
| چکیده | ||
| The eccentricity of a vertex $v$ is the maximum distance between $v$ and any other vertex. A vertex with maximum eccentricity is called a peripheral vertex. The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum of the distances between all pairs of peripheral vertices of $G.$ In this paper, we initiate the study of the peripheral Wiener index and we investigate its basic properties. In particular, we determine the peripheral Wiener index of the cartesian product of two graphs and trees. | ||
| کلیدواژه‌ها | ||
| Distance (in Graphs)؛ Wiener Index؛ Peripheral Wiener Index | ||
| مراجع | ||
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[1] J.A. Bondy and U.S.R. Murty, Graph theory with applications, The Macmillan Press Ltd., London, Basingstoke, 1976.
[2] A.A. Dobrynin, R. Entringer, and I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math. 66 (2001), no. 3, 211–249.
[3] A.A. Dobrynin, I. Gutman, S. Klavžar, and P. Zigert, ˇ Wiener index of hexagonal systems, Acta Appl. Math. 72 (2002), no. 3, 247–294.
[4] R.C. Entringer, D.E. Jackson, and D.A. Snyder, Distance in graphs, Czechoslovak Math. J. 26 (1976), no. 2, 283–296.
[5] I. Gutman, B. Furtula, and M. Petrović, Terminal wiener index, J. Math. Chem. 46 (2009), no. 2, 522–531. [6] B. Horvat, T. Pisanski, and M. Randić, Terminal polynomials and star-like graphs, MATCH Commun. Math. Comput. Chem. 60 (2008), no. 2, 493–512.
[7] W. Imrich, S. Klavžar, and Douglas F.R., Topics in graph theory : Graphs and their cartesian product, Wiley-Interscience, New York, 2000.
[8] M. Randić and J. Zupan, Highly compact 2d graphical representation of dna sequences, SAR QSAR Environ. Res. 15 (2004), no. 3, 191–205.
[9] M. Randić, J. Zupan, and D. Vikić-Topić, On representation of proteins by starlike graphs, J. Mol. Graph. Modell. 26 (2007), no. 1, 290–305.
[10] E.A. Smolenskii, E.V. Shuvalova, L.K. Maslova, I.V. Chuvaeva, and M.S. Molchanova, Reduced matrix of topological distances with a minimum number of independent parameters: distance vectors and molecular codes, J. Math. Chem. 45 (2009), no. 4, 1004–1020. [11] L. Volkmann, Fundamente der graphentheorie, Springer, Vienna, New York, 1996.
[12] H. Wiener, Structural determination of paraffin boiling points, J. Amer. Chem. Soc. 69 (1947), no. 1, 17–20.
[13] K.A. Zaretskii, Constructing a tree on the basis of a set of distances between the hanging vertices, Spekhi Math. Nauk. 20 (1965), no. 6, 90–92.
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