Detour Number of 1-Fault Connected Graphs

Article type: Research Article

Authors: Raghu, T. Venkata^{a; *} | Sundara Rajan, R.^{a; †} | Ramesh Babu, A.^a | Anil, S.^b

Affiliations: [a] Department of Mathematics, Hindustan Institute of Technology and Science, Chennai 603 103, India. [email protected] | [b] Department of Computer Science and Engineering, Hindustan Institute of Technology and Science, Chennai 603 103, India

Correspondence: [*] Address for correspondence: Flat No: 305, Bhupal Enclave, Bhupalnagar, Tadepalligudem 534 101, India.

Note: [†] This work is supported by Project No. 2/48(4)/2016/NBHM(R.P.)/R&D II/14082, National Board of Higher Mathematics (NBHM), Department of Atomic Energy (DAE), Government of India.

Abstract: A subset S of a connected graph G of order n is called a detour set of G if for every vertex x in G there exist vertices u; v in S such that x lie on a u – v detour path. The detour number dn(G) of a graph G is the minimum cardinality of a detour set. In this paper we compute the detour number of certain 1-fault connected planar graphs.

Keywords: Geodetic number, detour set, detour number, 1-fault connected graphs, Hanoi graph, Sierpiński graph

DOI: 10.3233/FI-2020-1894

Journal: Fundamenta Informaticae, vol. 172, no. 1, pp. 97-104, 2020