The convexity spectra of graphs

Tong, Lee‐Ing; Yen, Pei-Lan; Farrugia, Alastair

doi:10.1016/j.dam.2007.08.049

Cited by 9 publications

(2 citation statements)

References 4 publications

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“…Taking an interesting direction for the subject of convexity in oriented graphs, in [12], Tong, Yen and Farrugia introduced the concepts of convexity spectrum and strong convexity spectrum of a graph. For a nontrivial connected graph G, we define the convexity spectrum, S C (G), of a graph G, as the set of convexity numbers of all orientations of G, and the strong convexity spectrum, S SC (G), of a graph G as the set of convexity numbers of all strongly connected orientations of G. If G has no strongly connected orientation, then S SC (G) is empty.…”

Section: Theoremmentioning

confidence: 99%

The Strong Convexity Spectra of Grids

Araujo‐Pardo

Hernández-Cruz

Montellano-Ballesteros

2017

Graphs and Combinatorics

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Let D be a connected oriented graph. A set S ⊆ V (D) is convex in D if, for every pair of vertices x, y ∈ S, the vertex set of every xy-geodesic, (xy shortest directed path) and every yx-geodesic in D is contained in S. The convexity number, con(D), of a non-trivial oriented graph, D, is the maximum cardinality of a proper convex set of D. The strong convexity spectrum of the graph G, S SC (G), is the set {con(D) : D is a strong orientation of G}. In this paper we prove that the problem of determining the convexity number of an oriented graph is N P-complete, even for bipartite oriented graphs of arbitrary large girth, extending previous known results for graphs. We also determine S SC (P n 2P m ), for every pair of integers n, m ≥ 2.

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Section: Theoremmentioning

confidence: 99%

The Strong Convexity Spectra of Grids

Araujo‐Pardo

Hernández-Cruz

Montellano-Ballesteros

2017

Graphs and Combinatorics

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“…Further results related to geodesic convexity in directed graphs can be found in [39,50,62,67,102,107,122,174,179]. exists a partition of V (G) into p cliques we say that G is p-clique.…”

Section: Theorem 610 ([102]mentioning

confidence: 99%

Geodesic Convexity in Graphs

Pelayo¹

2013

SpringerBriefs in Mathematics

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SpringerBriefs in Mathematics showcases expositions in all areas of mathematics and applied mathematics. Manuscripts presenting new results or a single new result in a classical field, new field, or an emerging topic, applications, or bridges between new results and already published works, are encouraged. The series is intended for mathematicians and applied School of Agricultural Engineering of Barcelona

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Introduction

Pelayo¹

2013

Geodesic Convexity in Graphs

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The convexity spectra of graphs

Cited by 9 publications

References 4 publications

The Strong Convexity Spectra of Grids

The Strong Convexity Spectra of Grids

Geodesic Convexity in Graphs

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