On radially extremal graphs and digraphs, a survey

Ferdinand Gliviak

Mathematica Bohemica (2000)

  • Volume: 125, Issue: 2, page 215-225
  • ISSN: 0862-7959

Abstract

top
The paper gives an overview of results for radially minimal, critical, maximal and stable graphs and digraphs.

How to cite

top

Gliviak, Ferdinand. "On radially extremal graphs and digraphs, a survey." Mathematica Bohemica 125.2 (2000): 215-225. <http://eudml.org/doc/248666>.

@article{Gliviak2000,
abstract = {The paper gives an overview of results for radially minimal, critical, maximal and stable graphs and digraphs.},
author = {Gliviak, Ferdinand},
journal = {Mathematica Bohemica},
keywords = {extremal graphs; extremal digraphs; radius; radius of graphs; radius of digraphs; extremal graphs; extremal digraphs; radius},
language = {eng},
number = {2},
pages = {215-225},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On radially extremal graphs and digraphs, a survey},
url = {http://eudml.org/doc/248666},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Gliviak, Ferdinand
TI - On radially extremal graphs and digraphs, a survey
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 2
SP - 215
EP - 225
AB - The paper gives an overview of results for radially minimal, critical, maximal and stable graphs and digraphs.
LA - eng
KW - extremal graphs; extremal digraphs; radius; radius of graphs; radius of digraphs; extremal graphs; extremal digraphs; radius
UR - http://eudml.org/doc/248666
ER -

References

top
  1. F. Buckley, Self-centered graphs with a given radius, Proc. 10th S-E Conf. Combinatorics, Graph Theory and Computing. Boca Raton, 1979, pp. 211-215. (1979) Zbl0426.05034MR0561047
  2. F. Buckley F. Harary, Distance in Graphs, Addison-Wesley, New York, 1990, 335 pp. (1990) MR1045632
  3. L. Caccetta, On graphs that are critical with respect to the parameters: diameter, connectivity and edge-connectivity, Matematiche (Catania) 47 (1992), 213-229. (1992) Zbl0793.05079MR1275856
  4. G. Chartrand, Songlin Tian, Distance in digraphs, Mathematics and Computer Models, Preprint, 1991, 15 pp. (1991) MR1486881
  5. Yu Xiang Du, Lijie Shi, Xiaodong Zhao, The structure of upper radius critical graphs, J. Natur. Sci. Math. 36 (1996), 77-82. (1996) MR1627192
  6. R. D. Dutton S. R. Medidi. R. C. Brigham, Changing and unchanging the radius of a graph, Linear Algebra Appl. 217 (1995), 67-82. (1995) MR1322543
  7. P. Erdős J. Pach R. Pollack Z. Tuza, 10.1016/0095-8956(89)90066-X, J. Combin. Theory, Ser. B 47 (1989), 73-79. (1989) MR1007715DOI10.1016/0095-8956(89)90066-X
  8. L. Fajtlowicz, 10.1002/jgt.3190120409, J. Graph Theory 12 (1988), 529-533. (1988) MR0968749DOI10.1002/jgt.3190120409
  9. G. Sh. Fridman, On radially critical oriented graphs, Dokl. Akad. Nauk 212 (1973), 556-559. (In Russian.) (1973) MR0412008
  10. F. Gliviak, On radially critical graphs, Recent Advances in Graph Theory- Proc. Symp. Prague 1974. Academia, Praha, 1975, pp. 207-221. (1974) MR0384613
  11. F. Gliviak, On the structure of radially critical graphs, Graphs, Hypergraphs and Block Systems. Proc. Symp. Zielona Gora, Poland, 1976, pp. 69-73. (1976) Zbl0345.05121MR0384613
  12. F. Gliviak M. Knor L. Šoltés, On radially maximal graphs, Australasian J. Combin. 9 (1994), 275-284. (1994) MR1271207
  13. F. Gliviak M. Knor L. Šoltés, Two-radially maximal graphs with special centers, Math. Slovaca 45 (1995), 227-233. (1995) MR1361815
  14. F. Gliviak M. Knor, On radially extremal digraphs, Math. Bohem. 120 (1995), 41-55. (1995) MR1336945
  15. N. Graham F. Harary, Changing and unchanging the diameter of a hypercube, Discrete Appl. Math. 37/38 (1992), 265-274. (1992) MR1176857
  16. F. Harary, Changing and unchanging invariants for graphs, Bull. Malaysian Math. Soc. (2) 5 (1982), 73-78. (1982) Zbl0512.05035MR0700121
  17. F. Harary G. Thomassen, 10.1017/S0305004100052051, Math. Proc. Cambridge Philos. Soc. 79 (1976), 11-18. (1976) MR0414439DOI10.1017/S0305004100052051
  18. T. W. Haynes L. M. Lawson R. C. Brigham R. D. Dutton, Changing and unchanging of the graphical invariants: Minimum and maximum degree, maximum clique size, node independence number and edge independence number, Congr. Numer. 72 (1990), 239-252. (1990) MR1041828
  19. J. Harant, 10.1016/0012-365X(93)90306-E, Discrete Math. 122 (1993), 335-341. (1993) Zbl0787.05055MR1246688DOI10.1016/0012-365X(93)90306-E
  20. J. Harant H. Walther, 10.1016/0095-8956(81)90101-5, J. Combin. Theory, Ser. B 30 (1981), 113-117. (1981) MR0609604DOI10.1016/0095-8956(81)90101-5
  21. Katsumi Inoue, Radius of 3-connected graphs, SUT J. Math. 32 (1996), 83-90. (1996) MR1401106
  22. Sh. M. Ismailov, The number of arcs of a digraph of a given radius with a given number of vertices and strong components, Dokl. Akad. Nauk Azerbaidzhana 27 (1971), 8-12. (In Russian.) (1971) MR0294177
  23. Ju. Nishanov, On radially critical graphs with maximal diameter, Voprosy algebry, teorii chisel, diferencialnych i integralnych uravneniy. Samarkand State University, Samarkand, 1973, pp. 138-147. (In Russian.) (1973) 
  24. Ju. Nishanov, On two classes of radially critical graphs, Voprosy algebry i teorii chisel. Samarkand State University, Samarkand, 1980, pp. 16-22. (In Russian.) (1980) 
  25. Ju. Nishanov, On radially critical graphs with radius two, Modeli i algoritmy prikiadnoj matematiki. Samarkand, 1989. pp. 125-130. (In Russian.) (1989) 
  26. Ju. Nishanov, On unicyclic radially critical graphs, Voprosy algebry i teorii chisel. Samarkand State University. Samarkand, 1990. pp. 54-65. (In Russian.) (1990) 
  27. J. Plesnik, Graph Algorithms, Veda, Bratislava. 1983, 343 pp. (in Slovak.) (1983) 
  28. Tomomi Segawa, Radius increase caused by edge deletion, SUT J. Math. 30 (1994), 159-162. (1994) MR1311012
  29. Songlin Tian, Sum distance in digraphs, Congr. Numer. 78 (1990), 179 -192. (1990) MR1140482
  30. Songlin Tian, Ch. E. Williams, Detour distance in digraphs, Graph Theory and Applications. Proc. Int. Conference, vol. 2, Y. Alavi. A. Schweuk (eds.). John Wiiey and Sons, 1995, pp. 1155-1165. (1995) MR1405891
  31. V. G. Vizing, On the number of edges in a graph with given radius, Dokl. Akad. Nauk 173 (1967). 1245-1246. (In Russian.) (1967) MR0210622
  32. A. A. Zykov, Fundamentals of Graph Theory, Nauka. Moskva, 1987, 381 pp. (In Russian.) (1987) MR0909295

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.