The Triangular Line n-Sigraph of a Symmetric n-Sigraph
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An n-tuple (a₁, a₂, ..., an) is symmetric, if ak = an−k+1, 1≤ k ≤ n. Let Hn = {(a₁, a₂, ..., an) : ak ∈ {+, −}, ak = an−k+1, 1 ≤ k ≤ n} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair Sn = (G, σ) (Sn = (G, μ)), where G = (V,E) is a graph called the underlying graph of Sn and : E ! Hn (μ : V ! Hn) is a function. Analogous to the concept of the triangular line graph of a graph, the triangle line symmetric n-sigraph of a symmetric n-sigraph is defined. It is shown that for any symmetric n-sigraph Sn, its triangular line symmetric n-sigraph is i-balanced. We then give structural characterization of triangular line symmetric n-sigraphs. Further, we obtain some switching equivalence relationship between triangular line symmetric n-sigraph and line symmetric n-sigraph.
Abstract
An n-tuple (a₁, a₂, ..., an) is symmetric, if ak = an−k+1, 1≤ k ≤ n. Let Hn = {(a₁, a₂, ..., an) : ak ∈ {+, −}, ak = an−k+1, 1 ≤ k ≤ n} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair Sn = (G, σ) (Sn = (G, μ)), where G = (V,E) is a graph called the underlying graph of Sn and : E ! Hn (μ : V ! Hn) is a function. Analogous to the concept of the triangular line graph of a graph, the triangle line symmetric n-sigraph of a symmetric n-sigraph is defined. It is shown that for any symmetric n-sigraph Sn, its triangular line symmetric n-sigraph is i-balanced. We then give structural characterization of triangular line symmetric n-sigraphs. Further, we obtain some switching equivalence relationship between triangular line symmetric n-sigraph and line symmetric n-sigraph.
참고문헌 (13)
- L. W. Beineke, "Consistent graphs with signed points", Riv. Math. Sci. Econom. Sociale, 1, pp.81~88 (1978)
- 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)
- E. B. Jarrett, "Transformations of graphs and digraphs", 박사, pp.1991
- 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, Preprint", ~
- 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, "The Line n-sigraph of a symmetric n-sigraph, Southeast Asian Bulletin of Mathematics- To appear", ~
- T. Soz´ansky, "Enueration of weak isomorphism classes of signed graphs", J. Graph Theory, 4(2), pp.127~144 (1980)
- T. Zaslavsky, "Signed Graphs", Discrete Appl. Math., 4(1), pp.47~74 (1982)
- T. Zaslavsky, "A mathematical bibliography of signed and gain graphs and its allied areas", Electronic J. Combin., 8(1) (1998)