An incidence of an undirected graph G is a pair (v, e) where v is a vertex of G and e an edge of G incident with v. Two incidences (v, e) and (w, f) are adjacent if one of the following holds: (i) v = w, (ii) e = f or (iii) vw = e or f . An incidence coloring of G assigns a color to each incidence of G in such a way that adjacent incidences get distinct colors. In 2012, Yang [15] proved that ev...

In a large fuzzy rule-based system, a great dealof computation time is required for a fuzzy inference engine. A given fuzzy rule-based system is modeled as a fuzzy inference graph where each node in the graph corresponds to a relation representing a rule in the rule-based system. This paper presents algorithms to minimize the number of nodes in the graph using fuzzy operations as well as their ...

The concept of the strongest path plays a crucial role in fuzzy graph theory. In classical graph theory, all paths in a graph are strongest, with a strength value of one. In this article, we introduce Menger’s theorem for fuzzy graphs and discuss the concepts of strengthreducing sets and t-connected fuzzy graphs. We also characterize t-connected and t-arc connected fuzzy graphs. 2012 Elsevier I...

In this paper we study strongest paths in a fuzzy graph. A necessary and sufficient condition for an arc in a fuzzy graph to be a strongest path and a sufficient condition for a path in a fuzzy graph to be a strongest path are obtained. A characterization of δ−arcs and the relationship between fuzzy cutnodes and δ−arcs are also obtained. Also a characterization of blocks is obtained using stron...

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

For a given simple graph G = (V,E), we define an incidence as a pair (v, e), where vertex v ∈ V (G) is one of the ends of edge e ∈ E(G). Let us define a set of incidences I(G) = {(v, e) : v ∈ V (G)∧ e ∈ E(G)∧ v ∈ e}. We say that two incidences (v, e) and (w, f) are adjacent if one of the following holds: (i) v = w, e 6= f , (ii) e = f , v 6= w, (iii) e = {v, w}, f = {w, u} and v 6= u. By an inc...