The all-paths transit function of a graph

Manoj Changat; Sandi Klavžar; Henry Martyn Mulder

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 2, page 439-448
  • ISSN: 0011-4642

Abstract

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A transit function R on a set V is a function R V × V → 2 V satisfying the axioms u ∈ R ( u , v ) , R ( u , v ) = R ( v , u ) and R ( u , u ) = { u } , for all u , v ∈ V . The all-paths transit function of a connected graph is characterized by transit axioms.

How to cite

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Changat, Manoj, Klavžar, Sandi, and Mulder, Henry Martyn. "The all-paths transit function of a graph." Czechoslovak Mathematical Journal 51.2 (2001): 439-448. <http://eudml.org/doc/30646>.

@article{Changat2001,
abstract = {A transit function $R$ on a set $V$ is a function $R\:V\times V\rightarrow 2^\{V\}$ satisfying the axioms $u\in R(u,v)$, $R(u,v)=R(v,u)$ and $R(u,u)=\lbrace u\rbrace $, for all $u,v \in V$. The all-paths transit function of a connected graph is characterized by transit axioms.},
author = {Changat, Manoj, Klavžar, Sandi, Mulder, Henry Martyn},
journal = {Czechoslovak Mathematical Journal},
keywords = {all-paths convexity; transit function; block graph; all-paths convexity; transit function; block graph},
language = {eng},
number = {2},
pages = {439-448},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The all-paths transit function of a graph},
url = {http://eudml.org/doc/30646},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Changat, Manoj
AU - Klavžar, Sandi
AU - Mulder, Henry Martyn
TI - The all-paths transit function of a graph
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 2
SP - 439
EP - 448
AB - A transit function $R$ on a set $V$ is a function $R\:V\times V\rightarrow 2^{V}$ satisfying the axioms $u\in R(u,v)$, $R(u,v)=R(v,u)$ and $R(u,u)=\lbrace u\rbrace $, for all $u,v \in V$. The all-paths transit function of a connected graph is characterized by transit axioms.
LA - eng
KW - all-paths convexity; transit function; block graph; all-paths convexity; transit function; block graph
UR - http://eudml.org/doc/30646
ER -

References

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  6. The Interval Function of a Graph, Mathematical Centre Tracts 132, Mathematisch Centrum, Amsterdam, 1980. (1980) Zbl0446.05039MR0605838
  7. Transit functions on graphs, In preparation. Zbl1166.05019
  8. The induced path convexity, betweenness, and svelte graphs, Discrete Math (to appear). (to appear) MR1910118
  9. A characterization of the interval function of a connected graph, Czechoslovak Math.  J. 44(119) (1994), 173–178. (1994) MR1257943
  10. Characterizing the interval function of a connected graph, Math. Bohem. 123(2) (1998), 137–144. (1998) MR1673965
  11. Convex sets in graphs, Indian J. Pure Appl. Math. 15 (1984), 1065–1071. (1984) MR0765010
  12. Theory of Convex Structures, North Holland, Amsterdam, 1993. (1993) MR1234493

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