Abstract
We are considering the website network http://www.pantechsolutions.net/ of the web navigation of the customers. This website network can be representing as an intuitionistic fuzzy directed graph by means of considering the navigation of the customers. In this intuitionistic fuzzy directed graph, the links are considering as vertices and the path between the links are considering as edges. The weightage of each edge are considering as number of visitors getting the link from one link to another link (membership value), number of visitors not getting the link, i.e. under traffic from one link to another link (non-membership value) and drop off case (intuitionistic fuzzy index). For this graph we are determining the maximum, minimum energies and its upper, lower bounds.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anjali, N., Mathew, S.: Energy of a fuzzy graph. AFMI. 6, 455–465 [2013]
Atanassov, K.: Intuitionistic fuzzy sets: theory and applications. Heidelberg, New York, Physica-Verlag [1999]
Brankov, V., Stevanovic, D., Gutman, I.: Equienergetic chemical trees. J. Seb. Chem. Soc. 69, 549–553 [2004]
Chandrashekar, A., Smitha, M.: On maximum degree energy of a graph. Int. J. Contemp. Math. Sciences. 4(8), 385–396 [2009]
Chountas, P., Alzebdi, M.S., Shannon, A., Atanassov, K.: On intuitionistic fuzzy trees. 13thICIFS, Sofia, NIFS. 15(2), 30–32 [2009]
Deepa, G., Praba, B., Chandrasekaran, V.M.: Max-Min intuitionistic fuzzy matrix of an intuitionistic fuzzy graph. IJPAM 98(3), 375–387 [2015]
Gutman, I.: The energy of a graph. Ber. Math-Statist. Sekt. Forschungsz. Graz. 103, 1–22 [1978]
Gutman, I.: The energy of graph: old and new results. Betten, A., Kohnert, A., Laue, R., Wassermann A. [Eds.], Algebraic Combinatorics and Applications. Springer-Verlag, Berlin, 196–211 [2001]
Gutman, I., Polansky, O.E.: Mathematical concepts in organic chemistry. Springer-Verlag, Berlin [1986]
Koolen, J.H., Moulton, V., Gutman, I.: Improving the McClelland inequality for total π-electron energy. Chemical physics Letters. 320, 213–216 [2000]
McAllister, M.L.N.: Fuzzy introduction graphs. Comput. Math. Applic. 15(10), 871–886 [1988]
Mordeson, J.N.: Fuzzy line graphs. Pattern Recognition Letters. 14(5), 381–384, [1993]
Praba, B., Chandrasekaran, V.M., Deepa, G.: Energy of an intuitionistic fuzzy graph. Italian journal of pure and applied mathematics. 32, 431–444 [2014]
Shannon, A., Atanassov, K.: On a generalization of intuitionistic fuzzy graphs. NIFS. 12(1), 24–29 [2006]
Yeh, R.T., Bang, S.Y.: Fuzzy relations, fuzzy graphs and their applications to clustering analysis, cognitive and decision processes in fuzzy sets, Zadeh, L.A., Fu, K.S., Shimara, M.Eds, Academic Press, New York, 125–149, [1975]
Acknowledgements
I wish to thank my co-authors for their kind help and support in my research work throughout this paper. My heartfelt thanks to my institution for providing me infrastructural facilities and excellent resources to carry out my research in VIT University, Vellore.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Praba, B., Deepa, G., Chandrasekaran, V.M., Venkatesan, K., Rajakumar, K. (2018). Bounds of Extreme Energy of an Intuitionistic Fuzzy Directed Graph. In: Madhu, V., Manimaran, A., Easwaramoorthy, D., Kalpanapriya, D., Mubashir Unnissa, M. (eds) Advances in Algebra and Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01120-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-01120-8_11
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-01119-2
Online ISBN: 978-3-030-01120-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)