Switching equivalence in symmetric -sigraphs
0
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
An n-tuple (a1, a2, ..., an) is symmetric, if ak = an−k+1, 1 ≤ k≤ n. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair Sn = (G, б) (Sn = (G, μ)), where G = (V,E) is a graph called the underlying graph of Sn and [수식] : E → Hn (μ : V → Hn) is a function. Analogous to the concept of the common-edge sigraph of a sigraph, common-edge symmetric n-sigraph of a symmetric n-sigraph is defined. Further, we obtain some switching equivalent characterizations between common-edge symmetric n-sigraph, line symmetric n-sigraph and jump symmetric n-sigraph.
Abstract
An n-tuple (a1, a2, ..., an) is symmetric, if ak = an−k+1, 1 ≤ k≤ n. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair Sn = (G, б) (Sn = (G, μ)), where G = (V,E) is a graph called the underlying graph of Sn and [수식] : E → Hn (μ : V → Hn) is a function. Analogous to the concept of the common-edge sigraph of a sigraph, common-edge symmetric n-sigraph of a symmetric n-sigraph is defined. Further, we obtain some switching equivalent characterizations between common-edge symmetric n-sigraph, line symmetric n-sigraph and jump symmetric n-sigraph.
참고문헌 (17)
- L. W. Beineke, "Consistent graphs with signed points", Riv. Math. Sci. Econom. Sociale, 1, pp.81~88 (1978)
- H. J. Broersma, "Path graphs", J. Graph Theory, 13(4), pp.427~444 (1989)
- G. T. Chartrand, "Subgraph distance in graphs defined by edge transfers", Discrete mathematics, 170, pp.63~79 (1997)
- F. Harary, "Graph Theory" (1969), Addison-Wesley Publishing Co.
- F. Harary, "On the notion of balance of a signed graph", Michigan Math. J., 2, pp.143~146 (1953)
- V. R. Kulli, "On common-edge graphs", Karnatak University Journal: Science, 18, pp.321~324 (1973)
- R. Rangarajan, "Notions of balance in symmetric n-sigraphs", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 11(2), pp.145~151 (2008), 장전수학회
- F. S. Roberts, "On the problem of consistent marking of a graph", Linear Algebra and Appl., 217, pp.255~263 (1995)
- F. S. Roberts, "On Balanced signed graphs and consistent marked graphs", ~
- E. Sampathkumar, "Point signed and line signed graphs", Nat. Acad.sci. letters, 7(3), pp.91~93 (1984)
- E. Sampathkumar, "Jump symmetric n-sigraphs", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 11(1), pp.89~95 (2008), 장전수학회
- E. Sampathkumar, "Line nsigraph of a symmetric n-sigraph-Submitted", ~
- E. Sampathkumar, "Common edge signed graph of a signed graph-Submitted", ~
- S. K. Simic, "Graph equation Ln(G) = G", univ. Beograd publ. Electrostatic. Fak., Ser. Math Fiz, 498(541), pp.41~44 (1975)
- D. Sinha, "New frontiers in the theory of signed graphs", 박사, pp.2005
- T. Zaslavsky, "Signed Graphs", Discretes Appl. Math., 4(1), pp.47~74 (1982)
- T. Zaslavsky, "A Mathematical bibliography of Signed and Gain graphs and its allied areas", Electronic J. Combinatorics, 8(1) (1998)