# Some results on semi-total signed graphs

• Volume: 31, Issue: 4, page 625-638
• ISSN: 2083-5892

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## Abstract

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A signed graph (or sigraph in short) is an ordered pair $S=\left({S}^{u},\sigma \right)$, where ${S}^{u}$ is a graph G = (V,E), called the underlying graph of S and σ:E → +, - is a function from the edge set E of ${S}^{u}$ into the set +,-, called the signature of S. The ×-line sigraph of S denoted by ${L}_{×}\left(S\right)$ is a sigraph defined on the line graph $L\left({S}^{u}\right)$ of the graph ${S}^{u}$ by assigning to each edge ef of $L\left({S}^{u}\right)$, 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.

## How to cite

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Deepa Sinha, and Pravin Garg. "Some results on semi-total signed graphs." Discussiones Mathematicae Graph Theory 31.4 (2011): 625-638. <http://eudml.org/doc/270833>.

@article{DeepaSinha2011,
abstract = {A signed graph (or sigraph in short) is an ordered pair $S = (S^u,σ)$, where $S^u$ is a graph G = (V,E), called the underlying graph of S and σ:E → +, - is a function from the edge set E of $S^u$ into the set +,-, called the signature of S. The ×-line sigraph of S denoted by $L_×(S)$ is a sigraph defined on the line graph $L(S^u)$ of the graph $S^u$ by assigning to each edge ef of $L(S^u)$, 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.},
author = {Deepa Sinha, Pravin Garg},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {sigraph; semi-total line sigraph; semi-total point sigraph; balanced sigraph; consistent sigraph},
language = {eng},
number = {4},
pages = {625-638},
title = {Some results on semi-total signed graphs},
url = {http://eudml.org/doc/270833},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Deepa Sinha
AU - Pravin Garg
TI - Some results on semi-total signed graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2011
VL - 31
IS - 4
SP - 625
EP - 638
AB - A signed graph (or sigraph in short) is an ordered pair $S = (S^u,σ)$, where $S^u$ is a graph G = (V,E), called the underlying graph of S and σ:E → +, - is a function from the edge set E of $S^u$ into the set +,-, called the signature of S. The ×-line sigraph of S denoted by $L_×(S)$ is a sigraph defined on the line graph $L(S^u)$ of the graph $S^u$ by assigning to each edge ef of $L(S^u)$, 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.
LA - eng
KW - sigraph; semi-total line sigraph; semi-total point sigraph; balanced sigraph; consistent sigraph
UR - http://eudml.org/doc/270833
ER -

## References

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1. [1] B.D. Acharya, A characterization of consistent marked graphs, National Academy, Science Letters, India 6 (1983) 431-440.
2. [2] B.D. Acharya, A spectral criterion for cycle balance in networks, J. Graph Theory 4 (1981) 1-11, doi: 10.1002/jgt.3190040102.
3. [3] B.D. Acharya, Some further properties of consistent marked graphs, Indian J. Pure Appl. Math. 15 (1984) 837-842. Zbl0552.05053
4. [4] B.D. Acharya and M. Acharya, New algebraic models of a social system, Indian J. Pure Appl. Math. 17 (1986) 150-168.
5. [5] B.D. Acharya, M. Acharya and D. Sinha, Characterization of a signed graph whose signed line graph is s-consistent, Bull. Malays. Math. Sci. Soc. 32 (2009) 335-341. Zbl1176.05032
6. [6] M. Acharya, ×-line sigraph of a sigraph, J. Combin. Math. Combin. Comp. 69 (2009) 103-111. Zbl1213.05120
7. [7] M. Behzad and G.T. Chartrand, Line coloring of signed graphs, Element der Mathematik, 24 (1969) 49-52. Zbl0175.50302
8. [8] L.W. Beineke and F. Harary, Consistency in marked graphs, J. Math. Psychol. 18 (1978) 260-269, doi: 10.1016/0022-2496(78)90054-8. Zbl0398.05040
9. [9] L.W. Beineke and F. Harary, Consistent graphs with signed points, Riv. Math. per. Sci. Econom. Sociol. 1 (1978) 81-88.
10. [10] D. Cartwright and F. Harary, Structural Balance: A generalization of Heider's Theory, Psych. Rev. 63 (1956) 277-293, doi: 10.1037/h0046049.
11. [11] G.T. Chartrand, Graphs as Mathematical Models (Prindle, Weber and Schmid, Inc., Boston, Massachusetts, 1977). Zbl0384.05029
12. [12] M.K. Gill, Contribution to some topics in graph theory and its applications, Ph.D. Thesis, (Indian Institute of Technology, Bombay, 1983).
13. [13] F. Harary, On the notion of balanc signed graphs, Mich. Math. J. 2 (1953) 143-146, doi: 10.1307/mmj/1028989917.
14. [14] F. Harary, Graph Theory (Addison-Wesley Publ. Comp., Reading, Massachusetts, 1969).
15. [15] F. Harary and J.A. Kabell, A simple algorithm to detect balance in signed graphs, Math. Soc. Sci. 1 (1980/81) 131-136, doi: 10.1016/0165-4896(80)90010-4. Zbl0497.05056
16. [16] F. Harary and J.A. Kabell, Counting balanced signed graphs using marked graphs, Proc. Edinburgh Math. Soc. 24 (1981) 99-104, doi: 10.1017/S0013091500006398. Zbl0476.05043
17. [17] C. Hoede, A characterization of consistent marked graphs, J. Graph Theory 16 (1992) 17-23, doi: 10.1002/jgt.3190160104. Zbl0748.05081
18. [18] E. Sampathkumar, Point-signed and line-signed graphs, Karnatak Univ. Graph Theory Res. Rep. 1 (1973), also see Abstract No. 1 in Graph Theory Newsletter 2 (1972), Nat. Acad. Sci.-Letters 7 (1984) 91-93.
19. [19] E. Sampathkumar and S.B. Chikkodimath, Semitotal graphs of a graph-I, J. Karnatak Univ. Sci. XVIII (1973) 274-280. Zbl0287.05120
20. [20] D. Sinha, New frontiers in the theory of signed graph, Ph.D. Thesis (University of Delhi, Faculty of Technology, 2005).
21. [21] D.B. West, Introduction to Graph Theory (Prentice-Hall, India Pvt. Ltd., 1996). Zbl0845.05001
22. [22] T. Zaslavsky, A mathematical bibliography of signed and gain graphs and allied areas, Electronic J. Combinatorics #DS8 (vi+151pp)(1999) Zbl0898.05001
23. [23] T. Zaslavsky, Glossary of signed and gain graphs and allied areas, II Edition, Electronic J. Combinatorics, #DS9(1998). Zbl0898.05002
24. [24] T. Zaslavsky, Signed analogs of bipartite graphs, Discrete Math. 179 (1998) 205-216, doi: 10.1016/S0012-365X(96)00386-X. Zbl0890.05060

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