Double Geodetic Number of a Line Graph


  • Ayarlin Kirupa M. Manonmaniam Sundaranar University, Tirunelveli-627012
  • T. Jebaraj Manonmaniam Sundaranar University , Abishekapatti, Tirunelveli-627012, Tamilnadu



double geodetic number, line graph, cartesian product, vertex covering number


Any line graph L(G), whose vertices correspond to the edges of G(V, E) and two vertices in L(G) are adjacent if and only if the corresponding edges in G are adjacent. If there are vertices u, v in S such that x, y ∈ I[u, v] for any pair of vertices x, y in G, then the set S of vertices of G is said to be a double geodetic set of G. The lowest cardinality of a double geodetic set is represented by the double geodetic number dg(G). In this study, we determine double geodetic number of several line graphs’ double geodetic numbers.


F. Buckley and F. Harary , Distance in graphs , Addison-Wesley, Reading, MA (1990)

G. Chartrand , F. Harary and P. Zhang, On the geodetic number of a graph , Networks, 39(2002), 1-6.

F . Harary, Graph Theory ( Addision- Wesley, 1969).

A. P. Santhakumaran, T. Jebaraj, Double geodetic number of a graph, Discussiones Mathematicae, Graph Theory, 32(2012) 109 - 119.

Venkanagouda .M. Goundar, K. S. Asha Latha, Venkatesha, M. H. Mud-debihal, On the geodetic number of line graph , Int. J. Contemp. Math. Sciences, vol.7, No 46(2012), 2289 - 2295. 13

Venkanagouda .M. Goudar and K. S. Asha Latha, Venkatesha, Split Geodetic number of a Line Graph, International J. Math. Com-bin.Vol.3(2015), 81-87.

M.Venkatachalapathy, K.Kokila and B.Abarna, Some Trends In Line Graphs, Advances in Theoritical and Applied Mathematics. ISSN 0973-4554 Volume 11, Number 2(2016), pp. 171-178.

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