In this paper, integrity of fuzzy graph is defined. Integrity of special types of graphs with constant node strength and node strength sequences as (pn−1 1 , p2) is discussed. Also, integrity of regular fuzzy graph and complete fuzzy graph is presented.

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 2005, Hosseini Dolama et al. [...

The fuzzy graph approach is more powerful in cluster analysis than the usual graph – theoretic approach due to its ability to handle the strengths of arcs effectively. The concept of node-strength sequence is introduced and is studied in a complete fuzzy graph. Two new connectivity parameters in fuzzy graphs namely, fuzzy node connectivity ðjÞ and fuzzy arc connectivity ðj0Þ are introduced and ...

An incidence of G consists of a vertex and one of its incident edge in G. The incidence coloring problem is a variation of vertex coloring problem. The problem is to find the minimum number (called incidence coloring number) of colors assigned to every incidence of G so that the adjacent incidences are not assigned the same color. In this paper, we propose a linear time algorithm for incidence-...

A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. A bipolar fuzzy graph structure is a generalization of a bipolar fuzzy graph. In this paper, we present several different types of operations, including composition, Cartesian product, strong product, cross product, and lexicographic product on ...

Evaluative and comparative analysis among educational projects remains an issue for administration, program directors, instructors, and educational institutes. This study reports a fuzzy complexity model for educational projects, which has two primary aspects (technical aspects and transparency aspects). These aspects may not be measured precisely due to uncertain situations. Therefore, a fuzzy...

We show that the number of incidences between m distinct points and n distinct lines in R 4 is O (