8 research outputs found
Sign-Compatibility of Some Derived Signed Graphs
A signed graph (or sigraph in short) is an ordered pair S = (Su, σ), where Su is a graph G = (V, E), called the underlying graph of S and σ : E → {+1, −1} is a function from the edge set E of Su into the set {+1, −1}, called the signature of S. A sigraph S is sign-compatible if there exists a marking µ of its vertices such that the end vertices of every negative edge receive ‘−1’ marks in µ and no positive edge does so. In this paper, we characterize S such that its ×-line sigraphs, semi-total line sigraphs, semi-total point sigraphs and total sigraphs are sign-compatible
On •-Line Signed Graphs L<sub>•</sub>(S)
A signed graph (or sigraph for short) is an ordered pair S = (Su,σ), where Su is a graph, G = (V,E), called the underlying graph of S and σ : E → {+,−} is a function from the edge set E of Su into the set {+,−}. For a sigraph S its •-line sigraph, L•(S) is the sigraph in which the edges of S are represented as vertices, two of these vertices are defined adjacent whenever the corresponding edges in S have a vertex in common, any such L-edge ee′ has the sign given by the product of the signs of the edges incident with the vertex in e ∩ e′. In this paper we establish a structural characterization of •-line sigraphs, extending a well known characterization of line graphs due to Harary. Further we study several standard properties of •-line sigraphs, such as the balanced •-line sigraphs, sign-compatible •-line sigraphs and C-sign-compatible •-line sigraphs
Negation switching invariant signed graphs
A signed graph (or, in short) is a graph G in which each edge x carries a value called its sign. Given a sigraph S, the negation of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs and on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus') or `-' (`minus') to vertices of such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains . In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and are signed isomorphic
On •-Line Signed Graphs L•(S)
A signed graph (or sigraph for short) is an ordered pair S = (Su,σ), where Su is a graph, G = (V,E), called the underlying graph of S and σ : E → {+,−} is a function from the edge set E of Su into the set {+,−}. For a sigraph S its •-line sigraph, L•(S) is the sigraph in which the edges of S are represented as vertices, two of these vertices are defined adjacent whenever the corresponding edges in S have a vertex in common, any such L-edge ee′ has the sign given by the product of the signs of the edges incident with the vertex in e ∩ e′. In this paper we establish a structural characterization of •-line sigraphs, extending a well known characterization of line graphs due to Harary. Further we study several standard properties of •-line sigraphs, such as the balanced •-line sigraphs, sign-compatible •-line sigraphs and C-sign-compatible •-line sigraphs
On Some Properties of Addition Signed Cayley Graph <inline-formula><math display="inline"><semantics><msubsup><mo mathvariant="bold-sans-serif">Σ</mo><mi mathvariant="bold-italic">n</mi><mo mathvariant="bold">∧</mo></msubsup></semantics></math></inline-formula>
We define an addition signed Cayley graph on a unitary addition Cayley graph Gn represented by Σn∧, and study several properties such as balancing, clusterability and sign compatibility of the addition signed Cayley graph Σn∧. We also study the characterization of canonical consistency of Σn∧, for some n
On Some Properties of Addition Signed Cayley Graph Σn∧
We define an addition signed Cayley graph on a unitary addition Cayley graph Gn represented by Σn∧, and study several properties such as balancing, clusterability and sign compatibility of the addition signed Cayley graph Σn∧. We also study the characterization of canonical consistency of Σn∧, for some n
On Some Properties of Signed Cayley Graph <i>S<sub>n</sub></i>
We define the signed Cayley graph on Cayley graph Xn denoted by Sn, and study several properties such as balancing, clusterability and sign-compatibility of the signed Cayley graph Sn. Apart from it we also study the characterization of the canonical consistency of Sn, for some n