### Edge neighborhood signed graphs

P. Siva Kota Reddy, U. K. Misra
2014 Applied Mathematical Sciences
Given a graph Γ = (V, E) of order at least 3, the edge neighborhood graph N e (Γ) of a graph Γ has the edges of Γ as its vertices and two distinct edges of Γ are adjacent in N e (Γ) if, and only if, the corresponding edges are adjacent to a common edge in Γ. We initiate a study of edge neighborhood graphs and characterize graphs for which N e (Γ) ∼ = Γ and N e (Γ) ∼ = Γ. A signed graph is an ordered pair Σ = (Γ, σ), where Γ = (V, E) is a graph called underlying graph of Σ and σ : E → {+, −} is
more » ... σ : E → {+, −} is a function. Analogously, we define the edge neighborhood signed graph N e (Σ) of a signed graph Σ = (Γ, σ) as a signed graph N e (Σ) = (N e (Γ), σ ), where for any edge e 1 e 2 in N e (Γ), σ (e 1 e 2 ) = σ(e 1 )σ(e 2 ). In this paper, we characterize signed graphs Σ which are edge neighborhood signed graphs and obtained some properties of edge neighborhood signed graphs. Mathematics Subject Classification: 05C76, 05C22