On the geodetic number and related metric sets in Cartesian product graphs

Discrete Mathematics

Volumn 308, Issue 23, 2008, Pages 5555-5561

  Brešar, Boštjan ^a   Klavžar, Sandi ^a   Horvat, Aleksandra Tepeh ^a  

^a UNIVERSITY OF MARIBOR   (Slovenia)

Author keywords

Cartesian product; Contour set; Geodetic number; Geodetic set

Indexed keywords

GRAPH THEORY; PARALLEL PROCESSING SYSTEMS;

CARTESIAN PRODUCT; CARTESIAN PRODUCTS; CONTOUR SET; GEODETIC NUMBER; GEODETIC SET; GEODETIC SETS; GRAPH G; PRODUCT STRUCTURES; UPPER BOUNDS;

GEODESY;

EID: 53049096962     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2007.10.007     Document Type: Article

References (17)

1. B. Brešar, A. Tepeh Horvat, On the geodetic number of median graphs, Discrete Math., in press (doi:10.1016/j.disc.2007.07.119)
2. Buckley F., Harary F., and Quintas L.V. Extremal results on the geodetic number of a graph. Scientia 2A (1988) 17-26
3. Cáceres J., Márquez A., Oellermann O.R., and Puertas M.L. Rebuilding convex sets in graphs. Discrete Math. 297 (2005) 26-37
4. Cáceres J., Puertas M.L., Hernando C., Mora M., Pelayo I., and Seara C. Searching for geodetic boundary vertex sets. Electron. Notes Discrete Math. 19 (2005) 25-31
5. Cáceres J., Puertas M.L., Hernando C., Mora M., Pelayo I., and Seara C. On geodetic sets formed by boundary vertices. Discrete Math. 306 (2006) 188-198
6. Cagaanan G.B., and Canoy S.R. On the hull sets and hull number of the Cartesian product of graphs. Discrete Math. 287 (2004) 141-144
7. Cagaanan G.B., and Canoy S.R. On the hull number of the composition of graphs. Ars Combin. 75 (2005) 113-119
8. Canoy S.R., and Garces I.L.L. Convex sets under some graph operations. Graphs Combin. 18 (2002) 787-793
9. Chartrand G., Erwin D., Johns G.L., and Zhang P. Boundary vertices in graphs. Discrete Math. 263 (2003) 25-34
10. Chartrand G., Erwin D., Johns G.L., and Zhang P. On boundary vertices in graphs. J. Combin. Math. Combin. Comput. 48 (2004) 39-53
11. Chartrand G., Harary F., and Zhang P. Geodetic sets in graphs. Discuss. Math. Graph Theory 20 (2000) 129-138
12. Chartrand G., Harary F., and Zhang P. On the geodetic number of a graph. Networks 39 (2002) 1-6
13. Harary F., Loukakis E., and Tsouros C. The geodetic number of a graph. Math. Comput. Modelling 17 (1993) 89-95
14. Imrich W., and Klavžar S. Product Graphs: Structure and Recognition (2000), Wiley-Interscience, New York
15. C. Lu, The geodetic numbers of graphs and digraphs, manuscript, 2004
16. T. Jiang, I. Pelayo, D. Pritikin, Geodesic convexity and Cartesian products in graphs, manuscript, 2004
17. Mulder H.M. The Interval Function of a Graph. Math. Centre Tracts vol. 132 (1980), Mathematisch Centrum, Amsterdam