1987
DOI: 10.1016/s0195-6698(87)80024-0
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Signed Graphs Represented by D∞

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Cited by 22 publications
(19 citation statements)
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“…Let G be an edge-signed graph represented by a line system S. If S embeds into Z n for some n, then we say that G is integrally represented or that G has an integral representation. By Theorem 2, for an edge-signed graph G with λ 1 (G) −2, G has an integral representation if and only if G is represented by a subset of D n for some n, or equivalently, G is represented by D ∞ , in the sense of [18]. We record this observation as the following corollary.…”
Section: Edge-signed Graphs and Representationsmentioning
confidence: 93%
“…Let G be an edge-signed graph represented by a line system S. If S embeds into Z n for some n, then we say that G is integrally represented or that G has an integral representation. By Theorem 2, for an edge-signed graph G with λ 1 (G) −2, G has an integral representation if and only if G is represented by a subset of D n for some n, or equivalently, G is represented by D ∞ , in the sense of [18]. We record this observation as the following corollary.…”
Section: Edge-signed Graphs and Representationsmentioning
confidence: 93%
“…If there is an answer to the above in connection to these indecomposable line systems in C n , a study of the exceptional graphs could generalize the related work of Chawathe and G.R. Vijayakumar on signed graphs [17,22,21,5].…”
Section: Complex Unit Gain Graphsmentioning
confidence: 98%
“…In [17], Vijayakumar proved that any connected signed graph with smallest eigenvalue less than −2 has an induced signed subgraph with at most 10 vertices and smallest eigenvalue less than −2. As a consequence of this result, he showed the following: ) Let M be a real symmetric matrix, whose diagonal entries are 0 and off-diagonal entries are integers.…”
Section: A Forbidden Matrix Resultsmentioning
confidence: 99%