The double star sequences and the general second Zagreb index |
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| Author |
leonid.uk@gmail.com
Khmelnytsky National University, Khmelnytsky, Ukraine
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| Abstract |
For a simple graph we introduce notions of the double star sequence, the double star fre-
quently sequence and prove that these sequences are inverses of each other. As a consequence,
we express the general second Zagreb index in terms of the double star sequence. Also, we
calculate the ordinary generating function and a linear recurrence relation for the sequence of
the general second Zagreb indexes.
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| Keywords |
simple graph; double star sequence; general second Zagreb index
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| DOI |
doi:10.15330/ms.51.2.115-123
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| Reference |
1. B. Bollobas, P. Erdos, Graphs of extremal weights, Ars Comb. 50 (1998), 225-233.
2. G. Xavier, E. Suresh, I. Gutman, Counting relations for general Zagreb indices, Kragujevac Journal of Mathematics, 38 (2014), ¹1, 95.103. 3. L. Bedratyuk, O. Savenko, The Star Sequence and the General First Zagreb Index, MATCH Communications in Mathematical and in Computer Chemistry, 79 (2018), ¹2, 407-414. 4. J. Riordan, Combinatorial Identities, New York, Wiley, 1979. 5. T. Doslic, B. Furtula, A. Graovac, I. Gutman, S. Moradi, Z. Yarahmadi, On vertex-degree-based molecular structure descriptors, MATCH Commun. Math. Comput. Chem., 66 (2011), 613-626. 6. L. Comtet, Nombres de Stirling generaux et fonctions symetriques, C. R. Acad. Sci. Paris. Ser. A, 275 (1972), 747-750. 7. T. Mansour, M. Schork, Commutation Relations, Normal Ordering, and Stirling Numbers, CRC Press, 2015. 8. R. Graham, D. Knuth, O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, 1989. |
| Pages |
115-123
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| Volume |
51
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| Issue |
2
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| Year |
2019
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| Journal |
Matematychni Studii
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| Full text of paper | |
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