On The Fault Tolerant Geodetic Number Of Total And Middle Number Of A Graph
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Abstract
The total graph of a graph is a graph such that the vertex set of corresponds to the vertices and edges of and two vertices are adjacent in if and only if their corresponding element are either adjacent or incident in The middle graph of connected graph denoted by is the graph whose vertex set is where two vertices are adjacent if they are adjacent edges of or one is a vertex of and the other is an edge incident with it. In this article, we studied the fault tolerant geodetic number of total and middle graph of a graph.
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References
H.A. Ahangar, S. Kosari, S.M. Sheikholeslami and L. Volkmann, Graphs with
large geodetic number, Filomat, 29:6 (2015), 1361 – 1368.
H. Abdollahzadeh Ahangar, V. Samodivkin, S. M. Sheikholeslami and Abdollah
Khodkar, The restrained geodetic number of a graph, Bulletin of the Malaysian
Mathematical Sciences Society, 38(3), (2015), 1143-1155.
H. Abdollahzadeh Ahangar, Fujie-Okamoto, F. and Samodivkin, V., On the forcing
connected geodetic number and the connected geodetic number of a graph, Ars
Combinatoria, 126, (2016), 323-335.
D. Anusha, J. John and S. Joseph Robin, The geodetic hop domination number of
complementary prisms, Discrete Mathematics, Algorithms and Applications,13(6),
(2021),2150077.
S. Beula Samli, J John and S. Robinson Chellathurai, The double geo chromatic
number of a graph, Bulletin of the International Mathematical Virtual Institute 11
(1), (2021) 25-38.
F. Buckley and F.Harary, Distance in Graphs, Addition- Wesley, Redwood City,
CA, (1990).
G. Chartrand, P. Zhang, The forcing geodetic number of a graph, Discuss. Math.
Graph Theory, 19 (1999), 45–58.
G. Chartrand, F. Harary and P. Zhang, On the geodetic number of a graph, Networks,
39(1), (2002), 1 - 6.
T.W. Hayes, P.J. Slater and S.T. Hedetniemi, Fundamentals of domination in graphs,
Boca Raton, CA: CRC Press, (1998).
A. Hansberg and L.Volkmann, On the geodetic and geodetic domination numbers
of a graph, Discrete Mathematics, 310, (2010), 2140-2146.
J. John and D. Stalin, The edge geodetic self decomposition number of a graph
RAIRO-Operations Research 55, (2019), S1935-S1947
J. John and D. Stalin, Edge geodetic self-decomposition in graphs, Discrete Mathe-
matics, Algorithms and Applications 12 (05), (2020), 2050064
J. John, The forcing monophonic and the forcing geodetic numbers of a graph,
Indonesian Journal of Combinatorics .4(2), (2020) 114-125.
J. John and D.Stalin, Distinct edge geodetic decomposition in Graphs, Communic-
ation in Combinatorics and Optimization, 6 (2),(2021), 185-196
J .John, On the vertex monophonic, vertex geodetic and vertex Steiner numbers
of graphs, Asian-European Journal of Mathematics 14 (10), (2021), 2150171.
T. Jebaraj and . K. Bensiger , The upper and the forcing fault tolerent geodetic
number of a graph, Ratio Mathematica, 44 (2022) 167–174.
A.P. Santhakumaran and J. John, The connected edge geodetic number of a graph,
SCIENTIA Series A: Mathematical Sciences 17,(2009), 67-82
A.P. Santhakumaran and J. John, The upper edge geodetic number and the forcing
edge geodetic number of a graph, Opuscula Mathematica 29 (4), (2009), 427-441.
A. P. Santhakumaran and J. John, The upper connected edge geodetic number of
a graph, Filomat, 26(1), (2012), 131 - 141.
A.P. Santhakumaran and T. Jebaraj, Double geodetic number of a graph, Discussi-
ones Mathematicae, Graph Theory 32 (2012) 109–119
D. Stalin and J John, Edge geodetic dominations in graphs, Int. J. Pure Appl. Math,
116 (22), (2017), 31-40.