Abstract
The revised edge Szeged index of a connected graph G is defined as Sz∗ e (G) = X e=uv∈E(G) mu(e|G) + m0(e|G) 2 mv(e|G) + m0(e|G) 2 , where E(G) is the edge set of G, mu(e|G) is the number of edges closer to vertex u than to vertex v in G, mv(e|G) is the number of edges closer to vertex v than to vertex u in G, and m0(e|G) is the number of edges equidistant from both ends of e. We give a formula for the revised edge Szeged index of a bridge graph, from which the revised edge Szeged indices for several classes of graphs are calculated.
Keywords
Szeged index Revised edge Szeged index Revised Szeged index Bridge graphs Distance 2000 AMS Classification: 05 C 12
References
- Cai, X. and Zhou, B. Edge Szeged index of unicyclic graphs, MATCH Commun. Math. Comput. Chem. 63, 133–144, 2010. [2] Dong, H., Zhou, B. and Trinajsti´c, N. A novel version of the edge-Szeged index, Croat. Chem. Acta 84, 543–545, 2011.
- Gutman, I. A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes N. Y. 27, 9–15, 1994.
- Gutman, I. and Ashrafi, A. R. The edge version of the Szeged index, Croat. Chem. Acta 81, 263–266, 2008.
- Khadikar, P. V., Karmarkar, S., Agrawal, V. K., Singh, J., Shrivastava, A., Lukovits, I. and Diudea, M. V. Szeged index – Applications for drug modeling, Lett. Drug Design Disc. 2, 606–624, 2005.
- Khalifeh, M. H., Yousefi-Azari, H., Ashrafi, A. R. and Gutman, I. The edge Szeged index of product graphs, Croat. Chem. Acta 81, 277–281, 2008.
- Mansour, T. and Schork, M. The vertex PI index and Szeged index of bridge graphs, Discrete Appl. Math. 157, 1600–1606, 2009. [8] Mansour, T. and Trinajsti´c, N. The revised Szeged index of bridge graphs, to appear.
- Randi´c, M. On generalization of Wiener index to cyclic structures, Acta Chim. Slov. 49, 483-496, 2002.
- Trinajsti´c, N. Chemical Graph Theory, 2nd edn. (CRC Press, Boca Raton, 1992).
- Vukiˇcevi´c, D. Note on the graphs with the greatest edge-Szeged index, MATCH Commun. Math. Comput. Chem. 61, 673–681, 2009.
- Wiener, H. Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69, 7–20, 1947.
- Xing, R. and Zhou, B. On the revised Szeged index of bridge graphs, Comptes Rendus Math. 349, 489–492, 2011.
Abstract
References
- Cai, X. and Zhou, B. Edge Szeged index of unicyclic graphs, MATCH Commun. Math. Comput. Chem. 63, 133–144, 2010. [2] Dong, H., Zhou, B. and Trinajsti´c, N. A novel version of the edge-Szeged index, Croat. Chem. Acta 84, 543–545, 2011.
- Gutman, I. A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes N. Y. 27, 9–15, 1994.
- Gutman, I. and Ashrafi, A. R. The edge version of the Szeged index, Croat. Chem. Acta 81, 263–266, 2008.
- Khadikar, P. V., Karmarkar, S., Agrawal, V. K., Singh, J., Shrivastava, A., Lukovits, I. and Diudea, M. V. Szeged index – Applications for drug modeling, Lett. Drug Design Disc. 2, 606–624, 2005.
- Khalifeh, M. H., Yousefi-Azari, H., Ashrafi, A. R. and Gutman, I. The edge Szeged index of product graphs, Croat. Chem. Acta 81, 277–281, 2008.
- Mansour, T. and Schork, M. The vertex PI index and Szeged index of bridge graphs, Discrete Appl. Math. 157, 1600–1606, 2009. [8] Mansour, T. and Trinajsti´c, N. The revised Szeged index of bridge graphs, to appear.
- Randi´c, M. On generalization of Wiener index to cyclic structures, Acta Chim. Slov. 49, 483-496, 2002.
- Trinajsti´c, N. Chemical Graph Theory, 2nd edn. (CRC Press, Boca Raton, 1992).
- Vukiˇcevi´c, D. Note on the graphs with the greatest edge-Szeged index, MATCH Commun. Math. Comput. Chem. 61, 673–681, 2009.
- Wiener, H. Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69, 7–20, 1947.
- Xing, R. and Zhou, B. On the revised Szeged index of bridge graphs, Comptes Rendus Math. 349, 489–492, 2011.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | April 1, 2012 |
| Published in Issue | Year 2012 Volume: 41 Issue: 4 |