Some results on semi-total signed graphs

A signed graph (or sigraph in short) is an ordered pair ${\displaystyle S=(S^u,\sigma )}$, where ${\displaystyle S^u}$ is a graph G = (V,E), called the underlying graph of S and σ:E → {+, -} is a function from the edge set E of ${\displaystyle S^u}$ into the set {+,-}, called the signature of S. The ×-line sigraph of S denoted by ${\displaystyle L_{\times }\left(S\right)}$ is a sigraph defined on the line graph ${\displaystyle L\left(S^u\right)}$ of the graph ${\displaystyle S^u}$ by assigning to each edge ef of ${\displaystyle L\left(S^u\right)}$, the product of signs of the adjacent edges e and f in S. In this paper, first we define semi-total line sigraph and semi-total point sigraph of a given sigraph and then characterize balance and consistency of semi-total line sigraph and semi-total point sigraph.