On Van Degrees of Vertices and Van Indices of Graphs

Süleyman Ediz; Mesut Semiz

doi:doi:10.11648/j.mcs.20170204.11

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On Van Degrees of Vertices and Van Indices of Graphs

Süleyman Ediz, Mesut Semiz

Published in Mathematics and Computer Science (Volume 2, Issue 4)

Received: 11 May 2017 Accepted: 27 May 2017 Published: 7 July 2017

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Abstract

Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define two novel degree concepts for a vertex of a simple connected graph: Van degree and reverse Van degree. And also we define Van and reverse Van indices of a simple connected graph by using the Van degrees concepts. We compute the Van and reverse Van indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.

Published in	Mathematics and Computer Science (Volume 2, Issue 4)
DOI	10.11648/j.mcs.20170204.11
Page(s)	35-38
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Van Degrees, Reverse Van Degrees, Van Indices, Reverse Van Indices, Topological Indices, QSAR, QSPR

References

[1]	H. Wiener, Structural Determination of Paraffin Boiling Points, J. Am. Chem. Soc., 69, 17-20, 1947.
[2]	I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, 535-538, 1971.
[3]	I. Gutman, B. Ruščić, N. Trinajstić, C. N. Wilcox, Graph Theory and Molecular Orbitals. XII. Acyclic Polyenes, J. Chem. Phys. 62, 3399-3405, 1975.
[4]	M. Randić, On characterization of molecular branching, J. Amer. Chem. Soc. 97, 6609–6615, 1975.
[5]	Q. Cui, L. Zhong, The general Randić index of trees with given number of pendent vertices. Appl. Math. Comput. 302, 111–121, 2017.
[6]	Z. Chen, G. Su, L. Volkmann, Sufficient conditions on the zeroth-order general Randić index for maximally edge-connected graphs. Discrete Appl. Math. 218, 64–70, 2017.
[7]	W. Gao, M. K. Jamil, M. R. Farahani, The hyper-Zagreb index and some graph operations. J. Appl. Math. Comput. 54, 263–275, 2017.
[8]	S. Ediz, Reduced second Zagreb index of bicyclic graphs with pendent vertices. Matematiche (Catania) 71, 135–147, 2016.
[9]	S. Ediz, Maximum chemical trees of the second reverse Zagreb index. Pac. J. Appl. Math. 7, 287–291, 2015.
[10]	S. M. Hosamani, B. Basavanagoud, New upper bounds for the first Zagreb index. MATCH Commun. Math. Comput. Chem. 74, 97–101, 2015.
[11]	D. Vukicevic, J. Sedlar, D. Stevanovic, Comparing Zagreb Indices for Almost All Graphs, MATCH Commun. Math. Comput. Chem. 78, no. 2, 323-336, 2017.
[12]	M. Bianchi, A. Cornaro, J. L. Palacios, A. Torriero, New bounds of degree–based topological indices for some classes of c-cyclic graphs, Discr. Appl. Math. 184, 62–75, 2015.
[13]	K. C. Das, K. Xu, J. Nam, Zagreb indices of graphs, Front. Math. China 10, 567–582, 2015.
[14]	R. M. Tache, On degree–based topological indices for bicyclic graphs, MATCH Commun.
[15]	Math. Comput. Chem. 76, 99–116, 2016. E. Estrada, L. Torres, L. Rodríguez, I. Gutman, An atom-bond connectivity index: modelling the enthalpy of formation of alkanes. Indian J. Chem. 37A, 849–855, 1998.
[16]	L. Zhong, Q. Cui, On a relation between the atom bond connectivity and the first geometric arithmetic indices. Discrete Appl. Math., 185, 249–253, 2015.
[17]	A. R. Ashrafi, Z. T. Dehghan, N. Habibi, Extremal atom bond connectivity index of cactus graphs. Commun. Korean Math. Soc. 30, 283–295, 2015.
[18]	B. Furtula, Atom bond connectivity index versus Graovac Ghorbani analog. MATCH Commun. Math. Comput. Chem. 75, 233–242, 2016.
[19]	D. Dimitrov, On structural properties of trees with minimal atom bond connectivity index II: Bounds on and branches. Discrete Appl. Math. 204, 90–116, 2016.
[20]	X. M. Zhang, Y. Yang, H. Wang, X. D. Zhang, Maximum atom bond connectivity index with given graph parameters. Discrete Appl. Math. 215, 208–217, 2016.
[21]	D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges. J. Math. Chem. 46, 1369–1376, 2009.
[22]	Y. Yuan, B. Zhou, N. Trinajstić, On geometric arithmetic index. J. Math. Chem. 47, 833–841, 2010.
[23]	K. C. Das, On geometric arithmetic index of graphs. MATCH Commun. Math. Comput. Chem. 64, 619–630, 2010.
[24]	Z. Raza, A. A. Bhatti, A. Ali, More on comparison between first geometric arithmetic index and atom bond connectivity index. Miskolc Math. Notes 17, 561–570, 2016.
[25]	W. Gao, A note on general third geometric arithmetic index of special chemical molecular structures. Commun. Math. Res. 32, 131–141, 2016.
[26]	M. An, L. Xiong, G. Su, The k ordinary generalized geometric arithmetic index. Util. Math., 100; 383–405, 2016.
[27]	L. Zhong, The harmonic index for graphs. Applied Mathematics Letters. 25, 561–566, 2012.
[28]	J. Li, J. B. Lv, Y. Liu, The harmonic index of some graphs. Bull. Malays. Math. Sci. Soc. 39, 331–340, 2016.
[29]	A. Ilić, Note on the harmonic index of a graph. Ars Combin. 128, 295–299, 2016.
[30]	B. Zhou, N. Trinajstić, On a novel connectivity index. J. Math. Chem. 46, 1252–1270, 2009.
[31]	M. R. Farahani, Randić connectivity and sum connectivity indices for Capra designed of cycles. Pac. J. Appl. Math. 7, 11–17, 2015.
[32]	S. Akhter, M. Imran, Z. Raza, On the general sum connectivity index and general Randić index of cacti. J. Inequal. Appl. 300, 2016.

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APA Style

Süleyman Ediz, Mesut Semiz. (2017). On Van Degrees of Vertices and Van Indices of Graphs. Mathematics and Computer Science, 2(4), 35-38. https://doi.org/10.11648/j.mcs.20170204.11

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ACS Style

Süleyman Ediz; Mesut Semiz. On Van Degrees of Vertices and Van Indices of Graphs. Math. Comput. Sci. 2017, 2(4), 35-38. doi: 10.11648/j.mcs.20170204.11

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AMA Style

Süleyman Ediz, Mesut Semiz. On Van Degrees of Vertices and Van Indices of Graphs. Math Comput Sci. 2017;2(4):35-38. doi: 10.11648/j.mcs.20170204.11

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@article{10.11648/j.mcs.20170204.11,
  author = {Süleyman Ediz and Mesut Semiz},
  title = {On Van Degrees of Vertices and Van Indices of Graphs},
  journal = {Mathematics and Computer Science},
  volume = {2},
  number = {4},
  pages = {35-38},
  doi = {10.11648/j.mcs.20170204.11},
  url = {https://doi.org/10.11648/j.mcs.20170204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20170204.11},
  abstract = {Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define two novel degree concepts for a vertex of a simple connected graph: Van degree and reverse Van degree. And also we define Van and reverse Van indices of a simple connected graph by using the Van degrees concepts. We compute the Van and reverse Van indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.},
 year = {2017}
}

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TY  - JOUR
T1  - On Van Degrees of Vertices and Van Indices of Graphs
AU  - Süleyman Ediz
AU  - Mesut Semiz
Y1  - 2017/07/07
PY  - 2017
N1  - https://doi.org/10.11648/j.mcs.20170204.11
DO  - 10.11648/j.mcs.20170204.11
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 35
EP  - 38
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20170204.11
AB  - Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define two novel degree concepts for a vertex of a simple connected graph: Van degree and reverse Van degree. And also we define Van and reverse Van indices of a simple connected graph by using the Van degrees concepts. We compute the Van and reverse Van indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.
VL  - 2
IS  - 4
ER  -

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Author Information

Süleyman Ediz

Department of Mathematics Education, Faculty of Education, Yüzüncü Y?l University, Van, Turkey
Mesut Semiz

Department of Mathematics Education, Faculty of Education, Yüzüncü Y?l University, Van, Turkey

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Süleyman Ediz, Mesut Semiz. (2017). On Van Degrees of Vertices and Van Indices of Graphs. Mathematics and Computer Science, 2(4), 35-38. https://doi.org/10.11648/j.mcs.20170204.11

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ACS Style

Süleyman Ediz; Mesut Semiz. On Van Degrees of Vertices and Van Indices of Graphs. Math. Comput. Sci. 2017, 2(4), 35-38. doi: 10.11648/j.mcs.20170204.11

Copy | Download

AMA Style

Süleyman Ediz, Mesut Semiz. On Van Degrees of Vertices and Van Indices of Graphs. Math Comput Sci. 2017;2(4):35-38. doi: 10.11648/j.mcs.20170204.11

Copy | Download

@article{10.11648/j.mcs.20170204.11,
  author = {Süleyman Ediz and Mesut Semiz},
  title = {On Van Degrees of Vertices and Van Indices of Graphs},
  journal = {Mathematics and Computer Science},
  volume = {2},
  number = {4},
  pages = {35-38},
  doi = {10.11648/j.mcs.20170204.11},
  url = {https://doi.org/10.11648/j.mcs.20170204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20170204.11},
  abstract = {Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define two novel degree concepts for a vertex of a simple connected graph: Van degree and reverse Van degree. And also we define Van and reverse Van indices of a simple connected graph by using the Van degrees concepts. We compute the Van and reverse Van indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - On Van Degrees of Vertices and Van Indices of Graphs
AU  - Süleyman Ediz
AU  - Mesut Semiz
Y1  - 2017/07/07
PY  - 2017
N1  - https://doi.org/10.11648/j.mcs.20170204.11
DO  - 10.11648/j.mcs.20170204.11
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 35
EP  - 38
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20170204.11
AB  - Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define two novel degree concepts for a vertex of a simple connected graph: Van degree and reverse Van degree. And also we define Van and reverse Van indices of a simple connected graph by using the Van degrees concepts. We compute the Van and reverse Van indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.
VL  - 2
IS  - 4
ER  -

Copy | Download