Edges and vertices in a unique signed circle in a signed graph
نویسندگان
چکیده
منابع مشابه
The H - Line Signed Graph of a Signed Graph
A Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair S = (G,σ) (S = (G,μ)) where G = (V, E) is a graph called underlying graph of S and σ : E → (e1, e2, ..., ek) (μ : V → (e1, e2, ..., ek)) is a function, where each ei ∈ {+,−}. Particularly, a Smarandachely 2-signed graph or Smarandachely 2-marked graph is called abbreviated a signed graph or a marked graph. Given a ...
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A signed graph is a graph whose edges are signed. In a vertex-signed graph the vertices are signed. The latter is called consistent if the product of signs in every circle is positive. The line graph of a signed graph is naturally vertexsigned. Based on a characterization by Acharya, Acharya, and Sinha in 2009, we give constructions for the signed simple graphs whose naturally vertex-signed lin...
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In 1982, Zaslavsky introduced the concept of a proper vertex colouring of a signed graph G as a mapping φ : V (G) → Z such that for any two adjacent vertices u and v the colour φ(u) is different from the colour σ(uv)φ(v), where is σ(uv) is the sign of the edge uv. The substantial part of Zaslavsky’s research concentrated on polynomial invariants related to signed graph colourings rather than on...
متن کاملA note on a matrix criterion for unique colorability of a signed graph.
A signed graph, S, is colorable if its point set can be partitioned into subsets such that all positive lines join points of the same subset and all negative lines join points of different subsets. S is uniquely colorable if there is only one such partition. Developed in this note is a new matrix, called the type matrix of S, which provides a classification of the way pairs of points are joined...
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2017
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2017.03.004