Homomorphism and Isomorphism of Neutrosophic Over Topologized Graphs

Abstract

In 1965 Zadeh [12] was invent the idea of a fuzzy set as a mathematical frame work for representing vagueness and imprecise information. Rosenfield (1975) introduced the notion of fuzzy graph [10]. Fuzzy
graphs have numerous applications in diverse parts of science and engineering like broad cost communications
producing, social network. Attanassov introduced the concept of intuitionstic fuzzy set as a gerealization of
fuzzy sets [2]. Many researchers established and studied about fuzzy graphs and Intuitionstic fuzzy graphs
in[1].Neutrosophic set proposed by Smarandache [11,13,14] is a powerful tool for dealing incomplete , inconsistance, imprecision, uncertain, false and inderminate problems in the real world whenever the fuzzy and
intuitionstic fuzzy approches fail in such type of situation. Also he extended the neutrosophic set respectively to Neutrosophic Overset when some neutrosophic component is > 1, to Neutrosophic Underset when
some neutrosophic component is < 0, and to Neutrosophic Offset when some neutrosophic components are
off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 0. since
our real-world has numerous examples and applications of over-/under-/off-neutrosophic components[4,5,6].
Later, Narmada Devi [15,16,17,18,19,20,21,22,23] worked on new type of Neutrosophic over, Neutrosophic
off graph and minimal domination via Neutrosophic over graph and Neutrosophic over topologized graph. In
this paper, we introduce the notion of homomorphism and isomorphism between Neutrosophic over topologized graphs