Characterization of Line-Consistent Signed Graphs

• Autorzy: Daniel C. Slilaty , Thomas Zaslavsky
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 3
• Strony: 589-594

Daty

wydano

2015-08-01

otrzymano

2014-05-28

poprawiono

2014-12-14

zaakceptowano

2015-01-22

online

2015-07-29

Twórcy

autor

Daniel C. Slilaty

• Wright State University Dayton, OH 45435-0001, USA

autor

Thomas Zaslavsky

• Binghamton University (SUNY) Binghamton, NY 13902-6000, USA

Bibliografia

• [1] B.D. Acharya, A characterization of consistent marked graphs, Nat. Acad. Sci. Let- ters (India) 6 (1983) 431-440.
• [2] B.D. Acharya, Some further properties of consistent marked graphs, Indian J. Pure Appl. Math. 15 (1984) 837-842.
• [3] B.D. Acharya, M. Acharya and D. Sinha, Cycle-compatible signed line graphs, Indian J. Math. 50 (2008) 407-414.
• [4] B.D. Acharya, M. Acharya and D. Sinha, Characterization of a signed graph whose signed line graph is S-consistent , Bull. Malaysian Math. Sci. Soc. (2) 32 (2009) 335-341.
• [5] M. Acharya, ×-line signed graphs, J. Combin. Math. Combin. Comput. 69 (2009) 103-111.
• [6] M. Behzad and G. Chartrand, Line-coloring of signed graphs, Elem. Math. 24 (1969) 49-52.
• [7] L.W. Beineke and F. Harary, Consistent graphs with signed points, Riv. Mat. Sci. Econom. Social. 1 (1978) 81-88. doi:10.1002/jgt.3190160104[Crossref]
• [8] F. Harary, On the notion of balance of a signed graph, Michigan Math. J. 2 (1953-54) 143-146 and addendum preceding p. 1.
• [9] C. Hoede, A characterization of consistent marked graphs, J. Graph Theory 16 (1992) 17-23. doi:10.1002/jgt.3190160104[Crossref]
• [10] M. Joglekar, N. Shah and A.A. Diwan, Balanced group labeled graphs, Discrete Math. 312 (2012) 1542-1549. doi:10.1016/j.disc.2011.09.021[WoS][Crossref]
• [11] S.B. Rao, Characterizations of harmonious marked graphs and consistent nets, J. Comb. Inf. Syst. Sci. 9 (1984) 97-112.
• [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]
• [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.

Identyfikatory

DOI

10.7151/dmgt.1825