# Diameter-invariant graphs

Mathematica Bohemica (2005)

- Volume: 130, Issue: 4, page 355-370
- ISSN: 0862-7959

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topVacek, Ondrej. "Diameter-invariant graphs." Mathematica Bohemica 130.4 (2005): 355-370. <http://eudml.org/doc/249594>.

@article{Vacek2005,

abstract = {The diameter of a graph $G$ is the maximal distance between two vertices of $G$. A graph $G$ is said to be diameter-edge-invariant, if $d(G-e)=d(G)$ for all its edges, diameter-vertex-invariant, if $d(G-v)=d(G)$ for all its vertices and diameter-adding-invariant if $d(G+e)=d(e)$ for all edges of the complement of the edge set of $G$. This paper describes some properties of such graphs and gives several existence results and bounds for parameters of diameter-invariant graphs.},

author = {Vacek, Ondrej},

journal = {Mathematica Bohemica},

keywords = {extremal graphs; diameter of graph; distance; extremal graph; diameter of graph; distance},

language = {eng},

number = {4},

pages = {355-370},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Diameter-invariant graphs},

url = {http://eudml.org/doc/249594},

volume = {130},

year = {2005},

}

TY - JOUR

AU - Vacek, Ondrej

TI - Diameter-invariant graphs

JO - Mathematica Bohemica

PY - 2005

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 130

IS - 4

SP - 355

EP - 370

AB - The diameter of a graph $G$ is the maximal distance between two vertices of $G$. A graph $G$ is said to be diameter-edge-invariant, if $d(G-e)=d(G)$ for all its edges, diameter-vertex-invariant, if $d(G-v)=d(G)$ for all its vertices and diameter-adding-invariant if $d(G+e)=d(e)$ for all edges of the complement of the edge set of $G$. This paper describes some properties of such graphs and gives several existence results and bounds for parameters of diameter-invariant graphs.

LA - eng

KW - extremal graphs; diameter of graph; distance; extremal graph; diameter of graph; distance

UR - http://eudml.org/doc/249594

ER -

## References

top- Radius-invariant graphs, Math. Bohem. 129 (2004), 361–377. (2004) MR2102610
- Distance in Graphs, Addison-Wesley, Redwood City, 1990. (1990) MR1045632
- Changing and unchanging of the radius of graph, Linear Algebra Appl. 217 (1995), 67–82. (1995) MR1322543
- 10.1007/BF01844162, Aequationes Math. 4 (1970), 322–325. (1970) MR0281659DOI10.1007/BF01844162
- On radially extremal graphs and digraphs, a survey, Math. Bohem. 125 (2000), 215–225. (2000) Zbl0963.05072MR1768809
- On certain classes of graphs of diameter two without superfluous edges, Acta Fac. Rer. Nat. Univ. Comenianae, Math. 21 (1968), 39–48. (1968) MR0265197
- On the extension of graphs with a given diameter without superfluous edges, Mat. Cas. Slovensk. Akad. Vied 19 (1969), 92–101. (1969) MR0302503
- Changing and unchanging the diameter of a hypercube, Discrete Appl. Math. 37/38 (1992), 265–274. (1992) MR1176857
- Changing and unchanging invariants for graphs, Bull Malaysian Math. Soc. 5 (1982), 73–78. (1982) Zbl0512.05035MR0700121
- Design of diameter $e$-invariant networks, Congr. Numerantium 65 (1988), 89–102. (1988) Zbl0800.05011MR0992859
- Three classes of diameter $e$-invariant graphs, Comment. Math. Univ. Carolin. 28 (1987), 227–232. (1987) MR0904748
- Critical graphs of given diameter, Acta Fac. Rer. Nat. Univ. Comenianae, Math. 30 (1975), 71–93. (1975) MR0398904
- 10.1016/S0012-365X(03)00189-4, Discrete Math. 272 (2003), 119–126. (2003) MR2019205DOI10.1016/S0012-365X(03)00189-4

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