Signed Graphs with Fuzzy Labels and Their Energy

Résumé

Abstract: In a mapping η : E → {+, −} a fuzzy graph Γ(σ, μ) is said to be a fuzzy signed graph if each edge
is signed to {+ or −}. A vertex signed fuzzy graph is one in which each node has a signed value of {+ or −}.
The difference between positive degree and negative degree of a vertex is called signed degree of that vertex.
The notion of signed graphs with fuzzy labels is presented making use of signed degree. The adjacency matrix
and characteristic polynomial of several class of signed graphs with fuzzy labels are obtained. Additionally,
we find the spectra, energy, and some limitations of signed graphs with fuzzy labels.