Graph Equation for Line Graphs and m-Step Graphs
Given a graph G , the m-step graph of G , denoted by S m ( G ), has the same vertex set as G and an edge between two distinct vertices u and v if there is a walk of length m from u to v . The line graph of G , denoted by L ( G ), is a graph such that the vertex set of L ( G ) is the edge set of G an...
Gespeichert in:
| Veröffentlicht in: | Graphs and combinatorics 2012-11, Vol.28 (6), p.831-842 |
|---|---|
| Hauptverfasser: | , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | Given a graph
G
, the
m-step graph
of
G
, denoted by
S
m
(
G
), has the same vertex set as
G
and an edge between two distinct vertices
u
and
v
if there is a walk of length
m
from
u
to
v
. The
line graph
of
G
, denoted by
L
(
G
), is a graph such that the vertex set of
L
(
G
) is the edge set of
G
and two vertices
u
and
v
of
L
(
G
) are adjacent if the edges corresponding to
u
and
v
share a common end vertex in
G
. We characterize connected graphs
G
such that
S
m
(
G
) and
L
(
G
) are isomorphic. |
|---|---|
| ISSN: | 0911-0119 1435-5914 |
| DOI: | 10.1007/s00373-011-1081-7 |