Publication:
On characterizations of graphs having large geodetic numbers

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Issued Date

2022

Resource Type

Article

Language

eng

File Type

application/pdf

ISSN

23197234

Rights Holder(s)

Scopus

Bibliographic Citation

3 Biotech. Vol 12, No.7 (2022), p.-

Suggested Citation

Lumduanhom C., Khemmani V. On characterizations of graphs having large geodetic numbers. 3 Biotech. Vol 12, No.7 (2022), p.-. Retrieved from: https://hdl.handle.net/20.500.14740/9641

Title

On characterizations of graphs having large geodetic numbers

Author(s)

Lumduanhom C.
 Khemmani V.

Abstract

Let G be a nontrivial connected graph. For two vertices u and v of a graph G, the interval of u and v denoted by I(u, v) is the set containing all vertices lying on some u − v geodesic in G. Here a u − v geodesic is a path of length d(u, v). If S is a set of vertices of G, then I(S) is the union of all sets I(u, v) for vertices u and v in S. Now, if I(S) = V (G) then S is called a geodetic set of G and the geodetic number g(G) is the minimum cardinality among the geodetic sets of a graph G. In this research, we determine the geodetic number of complete multipartite graphs, wheels and cycles with one chord. Moreover, we characterize all connected graphs of order n having geodetic number n − 1. © SAS International Publications.

Subject(s)

Geodesic
 Geodetic number
 Geodetic set

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URI

https://hdl.handle.net/20.500.14740/9641

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Scopus: Year 2022

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