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2015 | OriginalPaper | Chapter

6. Open Problems

Authors : Kexiang Xu, Kinkar Ch. Das, Nenad Trinajstić

Published in: The Harary Index of a Graph

Publisher: Springer Berlin Heidelberg

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Abstract

Despite many interesting results on the Harary index and additively or multiplicatively weighted Harary index of graphs reported in the previous chapters, there are still some complicated and challenging problems, which remain open to us, on this topic.

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Literature
1.
go back to reference Xu K, Trinajstić N (2011) Hyper-Wiener and Harary indices of graphs with cut edges. Util Math 84:153–163MATHMathSciNet Xu K, Trinajstić N (2011) Hyper-Wiener and Harary indices of graphs with cut edges. Util Math 84:153–163MATHMathSciNet
3.
go back to reference Xu K, Liu M, Das KC, Gutman I, Furtula B (2014) A survey on graphs extremal with respect to distance-based topological indices. MATCH Commun Math Comput Chem 71:461–508MathSciNet Xu K, Liu M, Das KC, Gutman I, Furtula B (2014) A survey on graphs extremal with respect to distance-based topological indices. MATCH Commun Math Comput Chem 71:461–508MathSciNet
4.
go back to reference Xu K (2012) Trees with the seven smallest and eight greatest Harary indices. Discret Appl Math 160:321–331CrossRefMATH Xu K (2012) Trees with the seven smallest and eight greatest Harary indices. Discret Appl Math 160:321–331CrossRefMATH
5.
go back to reference Das KC, Xu K, Gutman I (2013) On Zagreb and Harary indices. MATCH Commun Math Comput Chem 70:301–314MATHMathSciNet Das KC, Xu K, Gutman I (2013) On Zagreb and Harary indices. MATCH Commun Math Comput Chem 70:301–314MATHMathSciNet
7.
go back to reference Gutman I (2002) Relation between hyper-Wiener and Wiener index. Chem Phys Lett 364:352–356CrossRef Gutman I (2002) Relation between hyper-Wiener and Wiener index. Chem Phys Lett 364:352–356CrossRef
8.
go back to reference Gutman I, Furtula B (2003) Hyper-Wiener index vs. Wiener index. Two highly correlated structure-descriptors. Monatshefte Math 134:975–981CrossRef Gutman I, Furtula B (2003) Hyper-Wiener index vs. Wiener index. Two highly correlated structure-descriptors. Monatshefte Math 134:975–981CrossRef
9.
go back to reference Zhou B, Gutman I (2004) Relations between Wiener, hyper-Wiener and Zagreb indices. Chem Phys Lett 394:93–95CrossRef Zhou B, Gutman I (2004) Relations between Wiener, hyper-Wiener and Zagreb indices. Chem Phys Lett 394:93–95CrossRef
10.
go back to reference Alizadeh Y, Iranmanesh A, Došlić T (2013) Additively weighted Harary index of some composite graphs. Discret Math 313:26–34CrossRefMATH Alizadeh Y, Iranmanesh A, Došlić T (2013) Additively weighted Harary index of some composite graphs. Discret Math 313:26–34CrossRefMATH
11.
go back to reference Xu K, Wang J, Das KC, Klavžar S (2014) Weighted Harary indices of apex trees and \(k\)-apex trees, manuscript Xu K, Wang J, Das KC, Klavžar S (2014) Weighted Harary indices of apex trees and \(k\)-apex trees, manuscript
12.
go back to reference Lepovic M, Gutman I (1998) A collective property of trees and chemical trees. J Chem Inf Comput Sci 38:823–826CrossRef Lepovic M, Gutman I (1998) A collective property of trees and chemical trees. J Chem Inf Comput Sci 38:823–826CrossRef
13.
go back to reference Goldman D, Istrail S, Piccolboni GLA (2000) Algorithmic strategies in combinatorial chemistry. In: Proceedings of the 11th ACM-SIAM symposium on discrete algorithms, pp 275–284 Goldman D, Istrail S, Piccolboni GLA (2000) Algorithmic strategies in combinatorial chemistry. In: Proceedings of the 11th ACM-SIAM symposium on discrete algorithms, pp 275–284
15.
go back to reference Li X, Wang L (2003) Solutions for two conjectures on the inverse problem of the Wiener index of peptoids. SIAM J Discret Math 17:210–218CrossRefMATH Li X, Wang L (2003) Solutions for two conjectures on the inverse problem of the Wiener index of peptoids. SIAM J Discret Math 17:210–218CrossRefMATH
16.
go back to reference Li X, Li Z, Wang L (2003) The inverse problems for some topological indices in combinatorial chemistry. J Comput Biol 10:47–55CrossRef Li X, Li Z, Wang L (2003) The inverse problems for some topological indices in combinatorial chemistry. J Comput Biol 10:47–55CrossRef
17.
go back to reference Xu K, Li J, Zhong L (2012) The Hosoya indices and Merrifield-Simmoms indices of graphs with connectivity at most \(k\). Appl Math Lett 25:476–480CrossRefMATHMathSciNet Xu K, Li J, Zhong L (2012) The Hosoya indices and Merrifield-Simmoms indices of graphs with connectivity at most \(k\). Appl Math Lett 25:476–480CrossRefMATHMathSciNet
18.
go back to reference Ivanciuc O, Balaban TS, Balaban AT (1993) Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices. J Math Chem 12:309–318CrossRefMathSciNet Ivanciuc O, Balaban TS, Balaban AT (1993) Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices. J Math Chem 12:309–318CrossRefMathSciNet
19.
go back to reference Plavšić D, Nikolić S, Trinajstić N, Mihalić Z (1993) On the Harary index for the characterization of chemical graphs. J Math Chem 12:235–250 Plavšić D, Nikolić S, Trinajstić N, Mihalić Z (1993) On the Harary index for the characterization of chemical graphs. J Math Chem 12:235–250
Metadata
Title
Open Problems
Authors
Kexiang Xu
Kinkar Ch. Das
Nenad Trinajstić
Copyright Year
2015
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-45843-3_6

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