Advances and Applications in Discrete Mathematics
Volume 27, Issue 1, Pages 73 - 84
(May 2021) http://dx.doi.org/10.17654/DM027010073 |
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LOCAL METRIC DIMENSION OF SOME WINDMILL GRAPHS AND SUNLET GRAPHS
V. Jude Annie Cynthia and V. F. Fancy
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Abstract: Let be a graph with vertex set V and edge set E. The study of minimum number of points in a graph which will distinguish all the adjacent vertices in terms of distance between the vertices is given by the local metric basis problem. A subset W of V is said to be a local metric basis of G, if for any two adjacent vertices there exists a vertex such that The minimum cardinality of local metric basis is called the local metric dimension of G and is denoted by In this paper, we have determined the local metric dimension of some windmill graphs and sunlet graphs. |
Keywords and phrases: metric dimension, local metric dimension, windmill graph, Dutch windmill graph, sunlet graph.
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