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Isomorphic properties of neighborly irregular vague graphs. (English) Zbl 1361.05083

Summary: The main purpose of this paper is to introduce weak isomorphism, co-weak isomorphism and isomorphism of neighborly irregular vague graphs. Some results on order, size and degree of nodes in isomorphic neighborly irregular and isomorphic highly irregular vague graphs are discussed. Isomorphism between neighborly irregular and highly irregular vague graphs are proved to be an equivalence relation. Density and balanced irregular vague graphs are introduced. Finally, an application of vague graphs is given.

MSC:

05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
05C72 Fractional graph theory, fuzzy graph theory
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[1] Akram, Certain types of vague graphs, University Politechnica of BucharestScientific Bulletin Series A 76 (1) pp 141– (2014)
[2] Alavi, Highly irregular graphs, J Graph Theory 11 (2) pp 235– (1987) · Zbl 0665.05043
[3] Borzooei, Ring sum in product in-tuitionistic fuzzy graphs, Journal of Advanced Research in Pure Mathematics 7 (1) pp 16– (2015)
[4] Gani, On regular fuzzy graphs, Journal of Physical Sciences 12 pp 33– (2008) · Zbl 1255.05155
[5] Gani, On irregular fuzzy graphs, Applied Mathematical Sciences 6 pp 517– (2012)
[6] Gau, Vague sets, IEEE Transactions on Systems, Man and Cybernetics 23 (2) pp 610– (1993) · Zbl 0782.04008
[7] Jun, Intuitionistic fuzzy subsemigroups and subgroups associated by intuitionistic fuzzy graphs, Commun Korean Math Soc 21 (3) pp 587– (2006) · Zbl 1161.05326
[8] Jun, Graphs based on BCK/BCI-Algebras, International Journal of Mathematics and Mathematical Sciences 2011 pp 8– (2011) · Zbl 1211.06012
[9] Kauffman, Introduction a la Theorie des Sous-Emsembles Flous (1973.)
[10] Ramakrishna, Vague graphs, International Journal of Computational Cognition 7 pp 51– (2009)
[11] Rashmanlou, Complete interval-valued fuzzy graphs, Annals of Fuzzy Mathematics and Informatics 6 (3) pp 677– (2013)
[12] Rashmanlou, Bipolar fuzzy graphs with categorical properties, International Journal of Computational Intelligent Systems 8 (5) pp 808– (2015)
[13] Rashmanlou, A study on bipolar fuzzy graphs, Journal of Intelligent and Fuzzy Systems 28 pp 571– (2015)
[14] Sunitha, Complement of a fuzzy graph, Indian Journal of Pure and Applied Mathematics 33 pp 1451– (2002) · Zbl 1013.05081
[15] Zadeh, Fuzzy sets, Information and Control 8 (3) pp 338– (1965) · Zbl 0139.24606
[16] Zadeh, Similarity relations and fuzzy ordering, Information Sciences 3 pp 177– (1971) · Zbl 0218.02058
[17] Zadeh, Is there a need for fuzzy logic, Information Sciences 178 pp 2751– (2008) · Zbl 1148.68047
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