On Eccentric Connectivity Index of Transformation Graphs
Abstract
The eccentric connectivity index is the sum of the product of eccentricity and degree of every vertex in G. In this paper, we present upper bounds for the total transformation graphs in terms of order, size and the first Zagreb index of the original graph G.
References
[2] M. Behzad, A criterion for the planarity of a total graph, Proc. Cambridge Phil. Soc.63 (1967) 679–681.
[3] Basavanagoud, B., Gutman, I., and Gali, C. S., (2015), On second Zagreb index and coindex of some derived graphs, Kragujevac J. Sci., 37, pp. 113–121.
[4] I. Gutman, N. Trinajstić (1972), Graph theory and molecular orbitals. Total Ԉ-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, pp. 535–538.
[5] F. Harary (1969), Graph Theory, Addison–Wesely, Reading.
[6] S. M. Hosamani, I. Gutman (2014), Zagreb indices of transformation graphs and total transformation graphs, Appl. Math. Comput., 247, pp. 1156-1160.
[7] S. M. Hosamani, B. Basavanagoud (2015), New upper bounds for the first Zagreb index, MATCH Commun. Math. Comput. Chem., 74(1), pp. 97–101.
[8] S. M. Hosamani, S. H. Malghan and I. N. Cangul, The first geometric-arithmetic index of graph operations, Advances and Applications in Mathematical Sciences, 14(6) (2015) 155–163.
[9] S. M. Hosamani, Computing Sanskruti index of certain nanostructures, J. Appl. Math. Comput. 1-9 (2016) DOI 10.1007/s12190-016-1016-9.
[10] S. M. Kang, M. A. Zahid, A. R. Virk, W. Nazeer, W. Gao, Calculating the degreebased topological indices of dendrimers, Open Chem. 16, 681–688 (2018).
[11] Nadeem, M.F., Zafar, S., Zahid, Z., (2015), Certain topological indicies of the line graph of subdivsion graphs, Appl. Math. Comput., (271), pp. 790–794.
[12] V. Sharma, R. Goswami, and A. K. Madan, Eccentric-connectivity index: A novel highly discriminating topological descriptor for structure-property and structure activity studies, J. Chem. Inf. Comput. Sci., 37(2)(1997)273–282.
[13] Su, G., Xu, L., (2015), Topological indices of the line graph of subdivision graphs and their Schur-bounds, Appl. Math. Comput., 253, pp. 395–401.
[14] Todeschini, R., Consonni, V., (2000), Handbook of Molecular Descriptors, WileyVCH, Weinheim.
[15] Ranjini, P.S., Lokesha, V., Cangul, I.N., (2011), On the Zagreb indices of the line graphs of the subdivision graphs, Appl. Math. Comput., 218, pp. 699–702.
[16] B. Wu, J. Meng, Basic properties of total transformation graphs, J. Math. Study 34(2001) 109-116.
[17] L. Xu, B. Wu, Transformation graph G−+−, Discrete Math. 308 (2008) 5144-5148.
[18] L. Yi. B. Wu, The transformation graph G++−, Australas. J. Comb. 44 (2009) 37–42.
To ensure uniformity of treatment among all contributors, other forms may not be substituted for this form, nor may any wording of the form be changed. This form is intended for original material submitted to AJCT and must accompany any such material in order to be published by AJCT. Please read the form carefully.
The undersigned hereby assigns to the Asian Journal of Convergence in Technology Issues ("AJCT") all rights under copyright that may exist in and to the above Work, any revised or expanded derivative works submitted to AJCT by the undersigned based on the Work, and any associated written, audio and/or visual presentations or other enhancements accompanying the Work. The undersigned hereby warrants that the Work is original and that he/she is the author of the Work; to the extent the Work incorporates text passages, figures, data or other material from the works of others, the undersigned has obtained any necessary permission. See Retained Rights, below.
AUTHOR RESPONSIBILITIES
AJCT distributes its technical publications throughout the world and wants to ensure that the material submitted to its publications is properly available to the readership of those publications. Authors must ensure that The Work is their own and is original. It is the responsibility of the authors, not AJCT, to determine whether disclosure of their material requires the prior consent of other parties and, if so, to obtain it.
RETAINED RIGHTS/TERMS AND CONDITIONS
1. Authors/employers retain all proprietary rights in any process, procedure, or article of manufacture described in the Work.
2. Authors/employers may reproduce or authorize others to reproduce The Work and for the author's personal use or for company or organizational use, provided that the source and any AJCT copyright notice are indicated, the copies are not used in any way that implies AJCT endorsement of a product or service of any employer, and the copies themselves are not offered for sale.
3. Authors/employers may make limited distribution of all or portions of the Work prior to publication if they inform AJCT in advance of the nature and extent of such limited distribution.
4. For all uses not covered by items 2 and 3, authors/employers must request permission from AJCT.
5. Although authors are permitted to re-use all or portions of the Work in other works, this does not include granting third-party requests for reprinting, republishing, or other types of re-use.
INFORMATION FOR AUTHORS
AJCT Copyright Ownership
It is the formal policy of AJCT to own the copyrights to all copyrightable material in its technical publications and to the individual contributions contained therein, in order to protect the interests of AJCT, its authors and their employers, and, at the same time, to facilitate the appropriate re-use of this material by others.
Author/Employer Rights
If you are employed and prepared the Work on a subject within the scope of your employment, the copyright in the Work belongs to your employer as a work-for-hire. In that case, AJCT assumes that when you sign this Form, you are authorized to do so by your employer and that your employer has consented to the transfer of copyright, to the representation and warranty of publication rights, and to all other terms and conditions of this Form. If such authorization and consent has not been given to you, an authorized representative of your employer should sign this Form as the Author.
Reprint/Republication Policy
AJCT requires that the consent of the first-named author and employer be sought as a condition to granting reprint or republication rights to others or for permitting use of a Work for promotion or marketing purposes.
GENERAL TERMS
1. The undersigned represents that he/she has the power and authority to make and execute this assignment.
2. The undersigned agrees to indemnify and hold harmless AJCT from any damage or expense that may arise in the event of a breach of any of the warranties set forth above.
3. In the event the above work is accepted and published by AJCT and consequently withdrawn by the author(s), the foregoing copyright transfer shall become null and void and all materials embodying the Work submitted to AJCT will be destroyed.
4. For jointly authored Works, all joint authors should sign, or one of the authors should sign as authorized agent
for the others.
Licenced by :
Creative Commons Attribution 4.0 International License.
