@article {
author = {Mathad, Veena and Narayankar, Kishori},
title = {On Lict sigraphs},
journal = {Transactions on Combinatorics},
volume = {3},
number = {4},
pages = {11-18},
year = {2014},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2014.5627},
abstract = {A signed graph (marked graph) is an ordered pair $S=(G,\sigma)$ $(S=(G,\mu))$, where $G=(V,E)$ is a graph called the underlying graph of $S$ and $\sigma:E\rightarrow\{+,-\}$ $(\mu:V\rightarrow\{+,-\})$ is a function. For a graph $G$, $V(G), E(G)$ and $C(G)$ denote its vertex set, edge set and cut-vertex set, 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 which two vertices are adjacent if and only if they correspond to adjacent 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 lict sigraphs, as a natural extension of the notion of lict graph to the realm of signed graphs. We show that every lict sigraph is balanced. We characterize signed graphs $S$ and $S^{'}$ for which $S\sim L_{c}(S)$, $\eta(S)\sim L_{c}(S)$, $L(S)\sim L_{c}(S')$, $J(S)\sim L_{c}(S^{'})$ 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.},
keywords = {signed graph,Line sigraph,Jump sigraph,Semitotal line sigraph,Lict sigraph},
url = {https://toc.ui.ac.ir/article_5627.html},
eprint = {https://toc.ui.ac.ir/article_5627_e7de2aef7c26e21d97bfaf79f2112406.pdf}
}