TY - JOUR
T1 - Base graph–connection graph
T2 - Dissection and construction
AU - Potočnik, Primož
AU - Verret, Gabriel
AU - Wilson, Stephen
N1 - Funding Information:
The first author is supported by Slovenian Research Agency , projects J1–1691 and P1–0294 . The second author is supported by the University of Western Australia as part of the Australian Research Council grant DE130101001 .
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2021/3/11
Y1 - 2021/3/11
N2 - This paper presents a phenomenon which sometimes occurs in tetravalent bipartite locally dart-transitive graphs, called a Base Graph–Connection Graph dissection. In this dissection, each white vertex is split into two vertices of valence 2 so that the connected components of the result are isomorphic. Given the Base Graph whose subdivision is isomorphic to each component, and the Connection Graph, which describes how the components overlap, we can, in some cases, provide a construction which can make a graph having such a decomposition. This paper investigates the general phenomenon as well as the special cases in which the connection graph has no more than one edge.
AB - This paper presents a phenomenon which sometimes occurs in tetravalent bipartite locally dart-transitive graphs, called a Base Graph–Connection Graph dissection. In this dissection, each white vertex is split into two vertices of valence 2 so that the connected components of the result are isomorphic. Given the Base Graph whose subdivision is isomorphic to each component, and the Connection Graph, which describes how the components overlap, we can, in some cases, provide a construction which can make a graph having such a decomposition. This paper investigates the general phenomenon as well as the special cases in which the connection graph has no more than one edge.
KW - 4-valent
KW - Arc-transitive
KW - Edge-transitive
KW - Graph
KW - Locally dart-transitive
KW - Semisymmetric
KW - Tetravalent
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U2 - 10.1016/j.dam.2020.10.028
DO - 10.1016/j.dam.2020.10.028
M3 - Article
AN - SCOPUS:85097912489
SN - 0166-218X
VL - 291
SP - 116
EP - 128
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -