A Study on Degrees of all Neighbors of a Vertex in Fuzzy Graphs

Abstract

. Graphs are one of the main tools for the mathematical modelling of various human problems. Fuzzy graphs clearly showed their ability to solve uncertain and ambiguous problems. Let G (cid:2) (cid:3)V, σ, μ(cid:8) be a fuzzy graph and u ∈ V . We define S (cid:12)(cid:13) (cid:3)u(cid:8) (cid:2) ∑ (cid:15)(cid:16)∈ℰ μ(cid:3)vu(cid:8)deg (cid:12) v . In this paper, we present some properties of S (cid:12)(cid:13) (cid:3)u(cid:8) on fuzzy graphs and establish relations between the Zagreb indices and the sum of the degrees of all neighbors of a vertex.