Split Restrained Geodetic Number of Strong Product and Lexicographic Product of Graphs

ASHALATHA K S

doi:10.36948/ijfmr.2023.v05i04.4492

Split Restrained Geodetic Number of Strong Product and Lexicographic Product of Graphs

Author(s)	ASHALATHA K S
Country	India
Abstract	Let ‘G’ be a graph. If u,v ∈V, then a u-v geodetic of G is the shortest path between u and v. The closed interval I[u, v] consists of all vertices lying in some u-v geodetic of G. For S⊆V(G) the set I[S] is the union of all sets I [u, v] for u,v∈S. A set S is a geodetic set of G if I[S]=V(G). The cardinality of minimum geodetic set of G is the geodetic number of G, denoted by g(G). A set S of vertices of a graph G is a split geodetic set if S is a geodetic set and 〈V-S〉 is disconnected, split geodetic number g_s (G) of G is the minimum cardinality of a split geodetic set of G. In this paper I study split restrained geodetic number of strong product and lexicographic product of graphs. A set S of vertices of a graph G is a split restrained geodetic set if S is a geodetic set and the subgraph 〈V-S〉 is disconnected with no isolated vertices. The minimum cardinality of a split restrained geodetic set of G is the split restrained geodetic number of G and is denoted by〖 g〗_sr (G). The split restrained geodetic numbers of some standard strong product and the lexicographic product of graphs are determined.
Keywords	Geodetic set, Geodetic number, Split geodetic set, Split geodetic number, Split Restrained Geodetic set, Split Restrained Geodetic number, Strong product, Lexicographic product of graphs.
Field	Mathematics
Published In	Volume 5, Issue 4, July-August 2023
Published On	2023-07-19
Cite This	Split Restrained Geodetic Number of Strong Product and Lexicographic Product of Graphs - ASHALATHA K S - IJFMR Volume 5, Issue 4, July-August 2023. DOI 10.36948/ijfmr.2023.v05i04.4492
DOI	https://doi.org/10.36948/ijfmr.2023.v05i04.4492
Short DOI	https://doi.org/gshm76

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Split Restrained Geodetic Number of Strong Product and Lexicographic Product of Graphs

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