An Upper Bound on the Radius of a 3VertexConnected C4Free Graph
Date
20200804Author
Fundikwa, Blessings T.
Mazorodze, Jaya P.
Mukwembi, Simon
Type
ArticleMetadata
Show full item recordAbstract
Let G=(V,E) be a finite, connected, undirected graph with vertex set V and edge set E. e distance dG (u,v) between two vertices u, v of G is the length of a shortest uv path in G.e eccentricity ec(v)of a vertex v∈V is the maximum distance between v and any other vertex in G. e value of the minimum eccentricity of the vertices of G is called the radius of G denoted by rad(G). e degree deg(v)of a vertex v of G is the number of edges incident with v. e minimum degree δ(G)is the minimum of the degrees of vertices in G.e open neighbourhood N(v)of a vertex v is the set of all vertices of G adjacent to v. e closed neighbourhood N[v]of v is the set N(v)∪v{ }. A graph is trianglefree if it does not contain C3 as a subgraph and C4−free if it does not contain C4 as a subgraph. For notions not defined, here we refer the reader to [1].
Additional Citation Information
Fundikwa, B. T., Mazorodze, J. P., & Mukwembi, S. (2020). An Upper Bound on the Radius of a 3VertexConnectedFree Graph. Journal of Mathematics, 2020.Publisher
HINDAWI
Subject
3vertexconnectedC4free graph
Connectivity measures
Vertexconnectivity
Edgeconnectivity
Additional Notes
The results in this paper are part of the first author’s MPhilSc thesis.
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