Characterization of Graphs of Connected Detour Number 2
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Authors: G. A. MOHAMMEDSALEH
DOI: 10.46793/KgJMat2301.119M
Abstract:
Let G = (V,E) be a connected graph of order P(G) ≥ 2. The connected detour number of G, denoted cdn(G), is introduced and studied by A. P. Santhakumaran and S. Athisayanathan [?]. In this paper, we characterize connected graph G of cdn(G) = 2 and of detour diameter D(G) = 5, 6.
Keywords:
Detour distance, detour number, connected detour number.
References:
[1] K. Abhishek and A. Ganesan, Detour distance pattern of a graph, International Journal of Pure and Applied Mathematics 87(5) (2013), 719–728.
[2] A. M. Ahmed and A. A. Ali, The connected detour numbers of special classes of connected graphs, J. Math. 20 (2019), 1–9.
[3] G. Chartrand, H. Escuadro and P. Zang, Detour distance in graph, J. Combin. Math. Combin. Copmut. 53 (2005), 75–94.
[4] G. Chartrand, L. Johns and P. Zang, Detour numbers of a graph, Util. Math. Combin. 64 (2003), 97–113.
[5] G. Chartrand and L. Lesnik, Graphs and Digraphs, 6th Edition, Taylor and Francis Group, CRC Press, New York, 2016.
[6] G. Chartrand and P. Zang, Distance in graphs-taking the long view, AKCE Int. J. Graphs Comb. 1(1) (2004), 1–13.
[7] A. P. Santhakumaran and S. Athisayanathan, On the connected detour number of a graph, J. Prime Res. Math. 5 (2009), 149–170.
[8] A. P. Santhakumaran and S. Athisayanathan, The connected detour number of a graph, J. Combin. Math. Combin. Copmut. 69 (2009), 205–218.
[9] A. P. Santhakumaran and P. Titus, The vertex detour number of a graph, AKCE Int. J. Graphs Comb. 4(1) 2007), 99–112.
[10] A. P. Santhakumaran and P. Titus, The connected vertex detour number of a graph, Acta Univ. Sapientiae Math. 2(2) (2010), 146–159.
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