On Lict sigraphs

A signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set $e(g)cup c(g)$ in whichtwo vertices are adjacent if and only if they correspond toadjacent edges of $g$ or one corresponds to an edge $e_{i}$ of $g$and the other corresponds to a cut-vertex $c_{j}$ of $g$ such that$e_{i}$ is incident with $c_{j}$. in this paper, we introduce lictsigraphs, as a natural extension of the notion of lict graph tothe realm of signed graphs. we show that every lict sigraph isbalanced. we characterize signed graphs $s$ and $s^{'}$ for which$ssim l_{c}(s)$, $eta(s)sim l_{c}(s)$, $l(s)sim l_{c}(s')$,$j(s)sim l_{c}(s^{'})$ and $t_{1}(s)sim l_{c}(s^{'})$, where$eta(s)$, $l(s)$, $j(s)$ and $t_{1}(s)$ are negation, line graph,jump graph and semitotal line sigraph of $s$, respectively, and$sim$ means switching equivalence.