# On •-Line Signed Graphs L•(S)

• Volume: 35, Issue: 2, page 215-227
• ISSN: 2083-5892

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## Abstract

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A signed graph (or sigraph for short) is an ordered pair S = (Su,σ), where Su is a graph, G = (V,E), called the underlying graph of S and σ : E → {+,−} is a function from the edge set E of Su into the set {+,−}. For a sigraph S its •-line sigraph, L•(S) is the sigraph in which the edges of S are represented as vertices, two of these vertices are defined adjacent whenever the corresponding edges in S have a vertex in common, any such L-edge ee′ has the sign given by the product of the signs of the edges incident with the vertex in e ∩ e′. In this paper we establish a structural characterization of •-line sigraphs, extending a well known characterization of line graphs due to Harary. Further we study several standard properties of •-line sigraphs, such as the balanced •-line sigraphs, sign-compatible •-line sigraphs and C-sign-compatible •-line sigraphs.

## How to cite

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Deepa Sinha, and Ayushi Dhama. "On •-Line Signed Graphs L•(S)." Discussiones Mathematicae Graph Theory 35.2 (2015): 215-227. <http://eudml.org/doc/271091>.

@article{DeepaSinha2015,
abstract = {A signed graph (or sigraph for short) is an ordered pair S = (Su,σ), where Su is a graph, G = (V,E), called the underlying graph of S and σ : E → \{+,−\} is a function from the edge set E of Su into the set \{+,−\}. For a sigraph S its •-line sigraph, L•(S) is the sigraph in which the edges of S are represented as vertices, two of these vertices are defined adjacent whenever the corresponding edges in S have a vertex in common, any such L-edge ee′ has the sign given by the product of the signs of the edges incident with the vertex in e ∩ e′. In this paper we establish a structural characterization of •-line sigraphs, extending a well known characterization of line graphs due to Harary. Further we study several standard properties of •-line sigraphs, such as the balanced •-line sigraphs, sign-compatible •-line sigraphs and C-sign-compatible •-line sigraphs.},
author = {Deepa Sinha, Ayushi Dhama},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {sigraph; line graph; •-line sigraph; balance; sign-compatibility; C-sign-compatibility; -line sigraph; -sign-compatibility},
language = {eng},
number = {2},
pages = {215-227},
title = {On •-Line Signed Graphs L•(S)},
url = {http://eudml.org/doc/271091},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Deepa Sinha
AU - Ayushi Dhama
TI - On •-Line Signed Graphs L•(S)
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 2
SP - 215
EP - 227
AB - A signed graph (or sigraph for short) is an ordered pair S = (Su,σ), where Su is a graph, G = (V,E), called the underlying graph of S and σ : E → {+,−} is a function from the edge set E of Su into the set {+,−}. For a sigraph S its •-line sigraph, L•(S) is the sigraph in which the edges of S are represented as vertices, two of these vertices are defined adjacent whenever the corresponding edges in S have a vertex in common, any such L-edge ee′ has the sign given by the product of the signs of the edges incident with the vertex in e ∩ e′. In this paper we establish a structural characterization of •-line sigraphs, extending a well known characterization of line graphs due to Harary. Further we study several standard properties of •-line sigraphs, such as the balanced •-line sigraphs, sign-compatible •-line sigraphs and C-sign-compatible •-line sigraphs.
LA - eng
KW - sigraph; line graph; •-line sigraph; balance; sign-compatibility; C-sign-compatibility; -line sigraph; -sign-compatibility
UR - http://eudml.org/doc/271091
ER -

## References

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