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## Discussiones Mathematicae Graph Theory

2011 | 31 | 4 | 625-638
Tytuł artykułu

### Some results on semi-total signed graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
625-638
Opis fizyczny
Daty
wydano
2011
otrzymano
2009-10-11
poprawiono
2010-09-30
zaakceptowano
2010-10-01
Twórcy
autor
• Centre for Mathematical Sciences, Banasthali University, Banasthali-304022, Rajasthan, India
autor
• Centre for Mathematical Sciences, Banasthali University, Banasthali-304022, Rajasthan, India
Bibliografia
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• [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] B.D. Acharya, Some further properties of consistent marked graphs, Indian J. Pure Appl. Math. 15 (1984) 837-842.
• [4] B.D. Acharya and M. Acharya, New algebraic models of a social system, Indian J. Pure Appl. Math. 17 (1986) 150-168.
• [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.
• [6] M. Acharya, ×-line sigraph of a sigraph, J. Combin. Math. Combin. Comp. 69 (2009) 103-111.
• [7] M. Behzad and G.T. Chartrand, Line coloring of signed graphs, Element der Mathematik, 24 (1969) 49-52.
• [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.
• [9] L.W. Beineke and F. Harary, Consistent graphs with signed points, Riv. Math. per. Sci. Econom. Sociol. 1 (1978) 81-88.
• [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] G.T. Chartrand, Graphs as Mathematical Models (Prindle, Weber and Schmid, Inc., Boston, Massachusetts, 1977).
• [12] M.K. Gill, Contribution to some topics in graph theory and its applications, Ph.D. Thesis, (Indian Institute of Technology, Bombay, 1983).
• [13] F. Harary, On the notion of balanc signed graphs, Mich. Math. J. 2 (1953) 143-146, doi: 10.1307/mmj/1028989917.
• [14] F. Harary, Graph Theory (Addison-Wesley Publ. Comp., Reading, Massachusetts, 1969).
• [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.
• [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.
• [17] C. Hoede, A characterization of consistent marked graphs, J. Graph Theory 16 (1992) 17-23, doi: 10.1002/jgt.3190160104.
• [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] E. Sampathkumar and S.B. Chikkodimath, Semitotal graphs of a graph-I, J. Karnatak Univ. Sci. XVIII (1973) 274-280.
• [20] D. Sinha, New frontiers in the theory of signed graph, Ph.D. Thesis (University of Delhi, Faculty of Technology, 2005).
• [21] D.B. West, Introduction to Graph Theory (Prentice-Hall, India Pvt. Ltd., 1996).
• [22] T. Zaslavsky, A mathematical bibliography of signed and gain graphs and allied areas, Electronic J. Combinatorics #DS8 (vi+151pp)(1999)
• [23] T. Zaslavsky, Glossary of signed and gain graphs and allied areas, II Edition, Electronic J. Combinatorics, #DS9(1998).
• [24] T. Zaslavsky, Signed analogs of bipartite graphs, Discrete Math. 179 (1998) 205-216, doi: 10.1016/S0012-365X(96)00386-X.
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Bibliografia
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