May 30, 2021 · Crisp set defines the value is either 0 or 1. Fuzzy set defines the value between 0 and 1 including both 0 and 1. It is also called a classical set. It specifies the degree to which …

Is there a standard procedure to define fuzzy generalizations of typical graph properties? Consider the concept of a fuzzy clique . Define the cliqueness $c(G)$ of a graph $G$ as the …

Dec 5, 2022 · This paper introduces a new concept of chromatic number (crisp) for a fuzzy graph G˜(V,E˜). Moreover, we define the operations of cap, join, difference, ring sum, direct product, …

Dec 5, 2022 · We focus on fuzzy graphs with crisp vertex sets and fuzzy edge sets. This paper introduces a new concept of chromatic number (crisp) for a fuzzy graph G˜ (V,E˜). Moreover, …

Nov 17, 2023 · This article presents a set of generalized ℘ -dependent formulae for fuzzy and crisp versions of various graph indices, including the first and second Zagreb indices, …

In this section, we define the concept of fuzzy chromatic polynomial of a fuzzy graph based on α-cuts of fuzzy graph which are crisp graphs. Furthermore, we determine the fuzzy chromatic …

We de ne the interval valued fuzzy graph (IVFG) associated with a crisp graph based on the degrees of the nodes of the crisp graph and study its various prop-erties. The nature of arcs of …

Abstract: This article presents a set of generalized ℘-dependent formulae for fuzzy and crisp versions of various graph indices, including the first and second Zagreb indices, harmonic …

A fuzzy graph G = ( 1, µ) is a pair of functions 1 : V → [0, 1] and µ : V ×V → [0, 1] such that µ(u, v) ≤ 1(u)∩(v) for all u, v in V where V is the vertex set. The fuzzy graph H = ( 2, ρ) is called a …

µ(x,y) ≤ σ(x) ∧ σ(y) for all x,y ∈ V,where ∧ stands for minimum. The underlying crisp graph of G is denoted by G∗: (σ∗,µ∗) where σ∗ = supp(σ) = {x ∈ V : σ(x) > 0} and µ∗ = supp(µ) = {(x,y) ∈ V× …