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    An Upper Bound on the Radius of a 3-Vertex-Connected C4-Free Graph

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    Fundikwa_Mazorodze_Mukwembi_An_Upper_Bound_on_the_Radius_of_a_3_Vertex_Connected_C4_Free_Graph.pdf (1.321Mb)
    Date
    2020-08-04
    Author
    Fundikwa, Blessings T.
    Mazorodze, Jaya P.
    Mukwembi, Simon
    Type
    Article
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    Abstract
    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 u-v 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 triangle-free 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].
    URI
    https://hdl.handle.net/10646/3964
    Additional Citation Information
    Fundikwa, B. T., Mazorodze, J. P., & Mukwembi, S. (2020). An Upper Bound on the Radius of a 3-Vertex-Connected-Free Graph. Journal of Mathematics, 2020.
    Publisher
    HINDAWI
    Subject
    3-vertex-connected
    C4-free graph
    Connectivity measures
    Vertex-connectivity
    Edge-connectivity
    Additional Notes
    The results in this paper are part of the first author’s MPhilSc thesis.
    Collections
    • Department of Mathematics Staff Publications [14]

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