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2018, vol. 42, br. 4, str. 533-537
Note on the unicyclic graphs with the first three largest wiener indices
(naslov ne postoji na srpskom)
aDžavni univerzitet u Novom Pazaru, Departman za matematičke nauke
bUniverzitet u Kragujevcu, Prirodno-matematički fakultet, Institut za matematiku i informatiku

e-adresaedinglogic@np.ac.rs, pavlovic@kg.ac.rs
Projekat:
Teorija grafova i matematičko programiranje sa primenama u hemiji i računarstvu (MPNTR - 174033)

Ključne reči: unicyclic graphs; Wiener index; distance; extremal graphs
Sažetak
(ne postoji na srpskom)
Let G = (V,E) be a simple connected graph with vertex set V and edge set E. Wiener index W(G) of a graph G is the sum of distances between all pairs of vertices in G, i.e., W(G) = Σ {u,v}cG dG(u, v), where dG(u, v) is the distance between vertices u and v. In this note we give more precisely the unicyclic graphs with the first tree largest Wiener indices, that is, we found another class of graphs with the second largest Wiener index.
Reference
Dobrynin, A.A., Entringer, R., Gutman, I. (2001) Wiener index of trees: Theory and applications. Acta Applicandae Mathematicae, 66(3): 211-249
Entringer, R.C., Jackson, D.E., Snyder, D.A. (1976) Distance in graph. Czechoslovak Math. J., 283-296; 26
Gutman, I., Potgieter, J.H. (1997) Wiener index and intermolecular forces. Journal of the Serbian Chemical Society, 62: 185-192
Hosoya, H. (1971) Topological Index. A Newly Proposed Quantity Characterizing the Topological Nature of Structural Isomers of Saturated Hydrocarbons. Bulletin of the Chemical Society of Japan, 44(9): 2332-2339
Hua, H. (2009) Wiener and Schultz molecular topological indices of graphs with specified cut edges. Communications in Mathematical and in Computer Chemistry / MATCH, vol. 61, br. 3, str. 643-651
Nikolić, S., Trinajstić, N., Mihalić, Z. (1995) The Wiener index: developments and applications. Croatica Chemica Acta, 105-129; 68
Rada, J. (2005) Variation of the Wiener index under tree transformations. Discrete Applied Mathematics, 148(2): 135-146
Šparl, P., Žerovnik, J. (2011) Graphs with given number of cut-edges and minimal value of Wiener number. International Journal of Chemical Modeling, 3(1-2); 131-137
Šparl, P., Žerovnik, J. (2012) Graphs extremal w.r.t. distance-based topological indices. u: Gutman I., Furtula B. [ur.] Distance in Molecular Graphs-Theory, Kragujevac: University of Kragujevac, pp. 177-194
Tang, Z., Deng, H. (2008) The (n,n)-graphs with the first three extremal Wiener indices. Journal of Mathematical Chemistry, 43(1): 60-74
Wiener, H. (1947) Structural determination of paraffin boiling points. Journal of the American Chemical Society, 69(1): 17-20
Xu, K., Liu, M., Das, K.C., Gutman, I., Furtula, B. (2014) A survey on graphs extremal with respect to distance-based topological indices. MATCH Commun. Math. Comput. Chem, 71, 461-508
 

O članku

jezik rada: engleski
vrsta rada: neklasifikovan
DOI: 10.5937/KgJMath1804533G
objavljen u SCIndeksu: 06.12.2018.

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