Certain types of m-polar interval-valued fuzzy graph

Abstract

In this paper, an unprecedented kind of fuzzy graph designated as m-polar interval valued fuzzy graph (m-PIVFG) is defined. Complement of the m-PIVFG open and closed neighborhood degrees of m-PIVFG are discussed. The other algebraic properties such as density, regularity, irregularity of the m-PIVFG are investigated. Moreover, some basic results on regularity and irregularity of m-PIVFG are proved. Free nodes and busy nodes of m-PIVFG is explored with some basic theorems and examples. Lastly, an application of m-PIVFG is described.

Domination of Bipolar Fuzzy Graphs in Various Settings

“…For a fuzzy graph G = (V, A, B) , Afsharmanesh and Borzooei [47] introduced the validity of edge uv ∈ E by (Note that in some literatures (see Samanta et al [48], and Mahapatra et al [49] and [50]) on the coloring of fuzzy graph, the above formulation is called the strength of edge.) The edge uv is valid if I(v, v � ) ≥ 1 2 , and otherwise call invalid. Furthermore, valid edge-based domination concepts are defined by Afsharmanesh and Borzooei [47]:…”

“…Fuzzy sets are used to describe the uncertainty of things, and are widely used in fuzzy reasoning, fuzzy intelligent decision-making systems and other fields, and thus have received widespread attention (see Bera and Pal [1] and [2], Islam and Pal [3], Samanta1 et al [4], Amanathulla et al [5], Pal et al [6], Prabakaran et al [7], Bagherinia et al [8], Gonzalez et al [9], and Maldonado et al [10]). On the other hand, graphs are an effective tool to describe the structured data.…”

On m-Polar Interval-valued Fuzzy Graph and its Application

“…We should feature that regarding this investigation, there are distinctive developing regions that we need not demonstrate here as they are outside of our feasible region. In any case, there can be interesting points for future research; for example, one may examine the m-PIVFG with various kinds of environments [39], e.g. domination, Pythagorean, fuzzy soft graph [40][41][42][43][44], etc.…”

Density of an $m$-bipolar fuzzy graph

“…Ramprasad et al [9] introduced the product m-polar fuzzy line and intersection graphs. Bera and pal [2] introduced the concept of m-polar interval-valued fuzzy graph and studied the algebraic properties of density, regularity and irregularity etc. on m-PIVFG.…”