# Characterization of Line-Consistent Signed Graphs

Daniel C. Slilaty; Thomas Zaslavsky

Discussiones Mathematicae Graph Theory (2015)

- Volume: 35, Issue: 3, page 589-594
- ISSN: 2083-5892

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topDaniel C. Slilaty, and Thomas Zaslavsky. "Characterization of Line-Consistent Signed Graphs." Discussiones Mathematicae Graph Theory 35.3 (2015): 589-594. <http://eudml.org/doc/271218>.

@article{DanielC2015,

abstract = {The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e., edge-signed graphs whose line graphs, with the naturally induced vertex signature, are consistent. Their proof applies Hoede’s relatively difficult characterization of consistent vertex-signed graphs. We give a simple proof that does not depend on Hoede’s theorem as well as a structural description of line-consistent signed graphs.},

author = {Daniel C. Slilaty, Thomas Zaslavsky},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {line-consistent signed graph; line graph; consistent vertex-signed graph; consistent marked graph.; consistent marked graph},

language = {eng},

number = {3},

pages = {589-594},

title = {Characterization of Line-Consistent Signed Graphs},

url = {http://eudml.org/doc/271218},

volume = {35},

year = {2015},

}

TY - JOUR

AU - Daniel C. Slilaty

AU - Thomas Zaslavsky

TI - Characterization of Line-Consistent Signed Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2015

VL - 35

IS - 3

SP - 589

EP - 594

AB - The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e., edge-signed graphs whose line graphs, with the naturally induced vertex signature, are consistent. Their proof applies Hoede’s relatively difficult characterization of consistent vertex-signed graphs. We give a simple proof that does not depend on Hoede’s theorem as well as a structural description of line-consistent signed graphs.

LA - eng

KW - line-consistent signed graph; line graph; consistent vertex-signed graph; consistent marked graph.; consistent marked graph

UR - http://eudml.org/doc/271218

ER -

## References

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- [12] F.S. Roberts and S. Xu, Characterizations of consistent marked graphs, Discrete Appl. Math. 127 (2003) 357-371. doi:10.1016/S0166-218X(02)00254-8[Crossref] Zbl1026.05054
- [13] T. Zaslavsky, Matrices in the theory of signed simple graphs, Advances in Discrete Mathematics and Applications: Mysore, 2008, B.D. Acharya, G.O.H. Katona, and J. Nesetril, Eds., Ramanujan Math. Soc., Mysore, India (2010) 207-229.
- [14] T. Zaslavsky, Consistency in the naturally vertex-signed line graph of a signed graph, Bull. Malaysian Math. Sci. Soc., to appear.

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