Functigraphs: An extension of permutation graphs

Andrew Chen; Daniela Ferrero; Ralucca Gera; Eunjeong Yi

Mathematica Bohemica (2011)

  • Volume: 136, Issue: 1, page 27-37
  • ISSN: 0862-7959

Abstract

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Let G 1 and G 2 be copies of a graph G , and let f : V ( G 1 ) → V ( G 2 ) be a function. Then a functigraph C ( G , f ) = ( V , E ) is a generalization of a permutation graph, where V = V ( G 1 ) ∪ V ( G 2 ) and E = E ( G 1 ) ∪ E ( G 2 ) ∪ { u v : u ∈ V ( G 1 ) , v ∈ V ( G 2 ) , v = f ( u ) } . In this paper, we study colorability and planarity of functigraphs.

How to cite

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Chen, Andrew, et al. "Functigraphs: An extension of permutation graphs." Mathematica Bohemica 136.1 (2011): 27-37. <http://eudml.org/doc/197079>.

@article{Chen2011,
abstract = {Let $G_1$ and $G_2$ be copies of a graph $G$, and let $f\colon V(G_1) \rightarrow V(G_2)$ be a function. Then a functigraph $C(G, f)=(V, E)$ is a generalization of a permutation graph, where $V=V(G_1) \cup V(G_2)$ and $E=E(G_1) \cup E(G_2)\cup \lbrace uv \colon u \in V(G_1), v \in V(G_2),v=f(u)\rbrace $. In this paper, we study colorability and planarity of functigraphs.},
author = {Chen, Andrew, Ferrero, Daniela, Gera, Ralucca, Yi, Eunjeong},
journal = {Mathematica Bohemica},
keywords = {permutation graph; generalized Petersen graph; functigraph; permutation graph; generalized Petersen graph; functigraph},
language = {eng},
number = {1},
pages = {27-37},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Functigraphs: An extension of permutation graphs},
url = {http://eudml.org/doc/197079},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Chen, Andrew
AU - Ferrero, Daniela
AU - Gera, Ralucca
AU - Yi, Eunjeong
TI - Functigraphs: An extension of permutation graphs
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 1
SP - 27
EP - 37
AB - Let $G_1$ and $G_2$ be copies of a graph $G$, and let $f\colon V(G_1) \rightarrow V(G_2)$ be a function. Then a functigraph $C(G, f)=(V, E)$ is a generalization of a permutation graph, where $V=V(G_1) \cup V(G_2)$ and $E=E(G_1) \cup E(G_2)\cup \lbrace uv \colon u \in V(G_1), v \in V(G_2),v=f(u)\rbrace $. In this paper, we study colorability and planarity of functigraphs.
LA - eng
KW - permutation graph; generalized Petersen graph; functigraph; permutation graph; generalized Petersen graph; functigraph
UR - http://eudml.org/doc/197079
ER -

References

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  1. Chartrand, G., Frechen, J. B., On the chromatic number of permutation graphs, Proof Tech. Graph Theory, Proc. 2nd Ann Arbor Graph Theory Conf. 1968 21-24 (1969). (1969) Zbl0199.59401MR0250934
  2. Chartrand, G., Harary, F., Planar permutation graphs, Ann. Inst. Henri. Poincaré, Nouv. Sér., Sect. B 3 433-438 (1967). (1967) Zbl0162.27605MR0227041
  3. Chartrand, G., Zhang, P., Introduction to Graph Theory, McGraw-Hill, Kalamazoo, MI (2004). (2004) 
  4. Hedetniemi, S., 10.1007/BFb0060115, Many Facets of Graph Theory, Proc. Conf. Western Michigan Univ., Kalamazoo/Mi. 1968, Lect. Notes Math. 110 171-189 (1969). (1969) Zbl0191.54905MR0250921DOI10.1007/BFb0060115
  5. Judson, T. W., Abstract Algebra: theory and applications, Boston, MA: PWS Publishing Company (1994). (1994) Zbl0823.00002

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