Some structural, metric and convex properties of the boundary of a graph
Let u;v be two vertices of a connected graph G . The vertex v is said to be a boundary vertex of u if no neighbor of v is further away from u than v . The boundary of a graph is the set of all its boundary vertices. In this work, we present a number of properties of the boundary of a graph under diÆ...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2013 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/20898 |
| Online Access: | https://hdl.handle.net/2117/20898 |
| Access Level: | Open access |
| Keyword: | Convex geometry Boundary Contour Extreme set Graph convexity Metric dimension. Geometria convexa Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Summary: | Let u;v be two vertices of a connected graph G . The vertex v is said to be a boundary vertex of u if no neighbor of v is further away from u than v . The boundary of a graph is the set of all its boundary vertices. In this work, we present a number of properties of the boundary of a graph under diÆerent points of view: (1) a realization theorem involving diÆerent types of boundary vertex sets: extreme set, periphery, contour, and the whole boundary; (2) the contour is a monophonic set; and (3) the cardinality of the boundary is an upper bound for both the metric dimension and the determining number of a graph |
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