Signed graphs with cut points whose positive inertia indexes are two.

A signed graph G σ consists of an underlying graph G and a sign function σ , which assigns each edge uv of G a sign σ ( u v ) , either positive or negative. The adjacency matrix of G σ is defined as A ( G σ ) = ( a u , v σ ) with a u , v σ = σ ( u v ) a u , v , where a u , v = 1 if u , v ∈ V ( G ) are adjacent, and a u , v = 0 otherwise. The positive inertia index of G σ , written as p ( G σ ) , is defined to be the number of positive eigenvalues of A ( G σ ) . Recently, Yu et al. (2016) [12] characterized the signed graphs G σ with pendant vertices such that p ( G σ ) = 2 . In this paper, we extend the above work to a more general case, characterizing the signed graphs G σ with cut points whose positive inertia index is 2. [ABSTRACT FROM AUTHOR]