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.
Collections
Related items
Showing items related by title, author, creator and subject.

The Gutman Index and the EdgeWiener Index of Graphs with given VertexConnectivity
Mazorodze, Jaya Percival; Mukwembi, Simon; Tomáš, Vetrík (University of Zielona Góra, 20151230)The Gutman index and the edgeWiener index have been extensively investigated particularly in the last decade. An important stream of re search on graph indices is to bound indices in terms of the order and other parameters ... 
Upper Bounds on the Diameter of Bipartite and TriangleFree Graphs with Prescribed Edge Connectivity
Fundikwa, Blessings T.; Mazorodze, Jaya P.; Mukwembi, Simon (HINDAWI, 20200903)Graph theory is used to study the mathematical structures of pairwise relations among objects. Mathematically, a pair G=(V,E) is a crisp graph, where V is a nonempty set and E is a relation on V[1]. e order of a graph G ... 
Average distance and edgeconnectivity I
Dankelmann, Peter; Mukwembi, Simon; Swart, Henda C (Society for Industrial and Applied Mathematics, 20150115)The average distance $\mu(G)$ of a connected graph G of order n is the average of the distances between all pairs of vertices of G. We prove that if G is a $\lambda$edgeconnected graph of order n, then the bounds $\mu(G) ...