Browse > Article
http://dx.doi.org/10.14317/jami.2015.545

DEGREE OF VERTICES IN VAGUE GRAPHS  

BORZOOEI, R.A. (Department of Mathematics, Islamic Azad University)
RASHMANLOU, HOSSEIN (Department of Mathematics, Islamic Azad University)
Publication Information
Journal of applied mathematics & informatics / v.33, no.5_6, 2015 , pp. 545-557 More about this Journal
Abstract
A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G1 and G2 using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.
Keywords
Cartesian product; tensor product; composition; normal product;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. Samanta and M. Pal, Fuzzy k-competition graphs and p-competition fuzzy graphs, Fuzzy Engineering and Information 5 (2013), 191-204.   DOI
2 S. Samanta and M. Pal, Irregular bipolar fuzzy graphs, International Journal of Application Fuzzy Sets 2 (2012), 91-102.   DOI
3 S. Samanta, T. Pramanik and M. Pal, Fuzzy colouring of fuzzy graphs, Afrika Matematika, DOI 10.1007/s13370-015-0317-8.   DOI
4 S. Samanta and M. Pal, Bipolar fuzzy hypergraphs, International Journal of Fuzzy Logic Systems 2 (2012), 17-28.   DOI
5 S. Samanta, M. Pal and A. Pal, Some more results on fuzzy k-competition graphs, International Journal of Advanced Research in Artificial Intelligence 3 (2014), 60-67.
6 S. Samanta and M. Pal, Some more results on bipolar fuzzy sets and bipolar fuzzy inter-section graphs, The Journal of Fuzzy Mathematics 22 (2014), 253-262.
7 L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.   DOI
8 L.A. Zadeh, Similarity relations and fuzzy ordering, Information Sciences 3 (1971), 177-200.   DOI
9 H. Rashmanlou and M. Pal, Balanced interval-valued fuzzy graph, Journal of Physical Sciences 17 (2013), 43-57.
10 M. Pal and H. Rashmanlou, Irregular interval-valued fuzzy graphs, Annals of Pure and Applied Mathematics 3 (2013), 56-66.
11 N. Ramakrishna, Vague graphs, International Journal of Computational Cognition 7 (2009), 51-58.
12 H. Rashmanlou and M. Pal, Antipodal interval-valued fuzzy graphs, International Journal of Applications of Fuzzy Sets and Artificial Intelligence 3 (2013), 107-130.
13 H. Rashmanlou and M. Pal, Some properties of highly irregular interval-valued fuzzy graphs, World Applied Sciences Journal 27 (2013), 1756-1773.
14 H. Rashmanlou and Y.B. Jun, Complete interval-valued fuzzy graphs, Annals of Fuzzy Mathematics and Informatics 6 (2013), 677-687.
15 H. Rashmanlou, S. Samanta, M. Pal and R.A. Borzooei, A study on bipolar fuzzy graphs, Journal of Intelligent and Fuzzy Systems 28 (2015), 571-580.
16 S. Samanta, M. Pal and A. Pal, New concepts of fuzzy planar graph, International Journal of Advanced Research in Articial Intelligence 3 (2014), 52-59.
17 A. Rosenfeld, Fuzzy graphs in Fuzzy Sets and Their Applications, L. A. Zadeh, K. S. Fu, and M. Shimura, Eds. Academic Press, New York, NY, USA, (1975), 77-95.
18 S. Samant and M. Pal, Fuzzy tolerance graphs, International Journal Latest Trend Mathematics 1 (2011), 57-67.
19 S. Samanta and M. Pal, Fuzzy threshold graphs, CiiT International Journal of Fuzzy Systems 3 (2011), 360-364.
20 M. Akram, M. Murtaza Yousaf and Wieslaw A. Dudek, Regularity in vague intersection graphs and vague line graphs, Abstract and Applied Analysis 2014, Article ID 525389, doi:10.1155/2014/525389.   DOI
21 Sk. Md. Abu Nayeem and M. Pal, The p-center problem on fuzzy networks and reduction of cost, Iranian Journal of Fuzzy Systems 5 (2008), 1-26.
22 M. Akram, N. Gani and A. Borumand Saeid, Vague hypergraphs, Journal of Intelligent and Fuzzy Systems 26 (2014), 647-653.
23 M. Akram, F. Feng, S. Sarwar and Y.B. Jun, Certain types of vague graphs, University Politehnica of Bucharest Scientific Bulletin Series A 76 (2014), 141-154.
24 W.L. Gau and D.J. Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cybernetics 23 (1993), 610-614.   DOI
25 A. Kauffman, Introduction a la Theorie des Sous-Emsembles Flous, 1 (1973) Masson et Cie.
26 J.N. Mordeson and P.S. Nair, Fuzzy Graphs and Fuzzy Hypergraphs, Physica Verlag, 2000.