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 .

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

VL - 291

SP - 116

EP - 128

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -