Title: Graphs in which G − N[v] is a cycle for each vertex v
Abstract: We say that G has the property P if G−N[v] is a cycle for any vertex v∈V(G), where N[v] is the closed neighborhood of v in G. For an integer l∈{3,4,5,6}, let Gl be a set of graphs defined as follows: G3={2K3}∪{G:both G and G‾ are connected, and G‾ is a triangle-free cubic graph}, where H‾ denotes the complement of H, G4={L(H)‾:H is a connected triangle-free cubic graph}, where L(H) denotes the line graph of H, G5={G20‾}, where G20 is the icosahedron, G6={G(5,2)}, where G(5,2) is the Petersen graph. Furthermore, let G={G1∨G2∨⋯∨Gt:Gi∈⋃l∈{3,4,5,6}Gl, t is any positive integer}. We show that a graph G has the property P if and only if G∈G.
Publication Year: 2021
Publication Date: 2021-06-21
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 6
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