Non Split Geodetic Number of a Line Graph
cartesian product, distance, edge covering number, line graph, non split geodetic number, vertex covering number., vertex covering number
Abstract
A set S V [L(G)] is a non split geodetic set of L(G), if S is a geodetic set and is connected. The non split geodetic number of a line graph L(G), is denoted by g [L(G)], is the minimum cardinality of a non split geodetic set of L(G). In this paper we obtain the non split geodetic number of line graph of any graph. Also obtain many bounds on non split geodetic number in terms of elements of G and covering number of G. We investigate the relationship between non split geodetic number and geodetic number.
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References
Gary Chartrand, Frank Harary, Ping Zhang (2002) On the geodetic number of a graph.Networks. 39(1), 1-6. https://doi.org/10.1002/net.10007
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M. Venkanagouda, K. Goudar, Ashalatha, M. Venkatesha (2012) Venkanagouda.M.Goudar,K.S.Ashalatha,Venkatesha, M.H.Muddebihal,On the Geodetic Number of Line Graph, Int.J.Contemp.Math.Sciences,vol. 7(46), 2289-2295.
M. Venkanagouda, Tejaswini Goudar, Venkatesha Non Split Geode- tic Number of a Graph.
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2013-10-30
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