A dominating set S of vertices of a graph G without isolated vertices is an independent semitotal... more A dominating set S of vertices of a graph G without isolated vertices is an independent semitotal dominating set if it is an independent dominating set and to each u in S there is a v in S at a distance exactly two. The independent semitotal domination number of a graph is the minimum size of an independent semitotal dominating set of vertices in G. In this paper, we have obtained the bounds for independent semitotal domination number in the Cartesian product of paths, path with a cycle and cycles.
A dominating set S of vertices of G without isolated vertices is an independent semitotal dominat... more A dominating set S of vertices of G without isolated vertices is an independent semitotal dominating set of G if S is an independent dominating set and to each u in S there is a v in S at a distance exactly two. The minimum and maximum cardinality of a minimal independent semitotal dominating set is called independent semitotal domination number and upper independent semitotal domination number of G, denoted by it2(G) and Γit2(G) respectively. The independent semitotal domination subdivision number sd it2(G) as the minimum number of edges to be subdivided (where no edge can be subdivided more than once) to increase the independent semitotal domination number. In this paper independent semitotal domination number and subdivision number with respect to this parameter of some special graphs are determined and studied.
International Journal of Mathematics Trends and Technology, Dec 29, 2023
A subset S of vertices of a graph G with no isolated vertices is an independent semitotal dominat... more A subset S of vertices of a graph G with no isolated vertices is an independent semitotal dominating set if S is an independent dominating set, and for each u S there is a v S at a distance exactly two. The independent semitotal domination number of a graph is the minimum size of an independent semitotal dominating set of vertices in G and is denoted by γit2(G). This paper initiates the study of independent semitotal bondage number of graphs. The independent semitotal bondage number denoted by bit2(G), is the minimum number of edges whose removal from the graph increases the independent semitotal domination number.
Journal of information & optimization sciences, 2024
In this paper a slight different parameter, independent semitotal domination number- This paramet... more In this paper a slight different parameter, independent semitotal domination number- This parameter lies between ( ) i G and 0 ( ) G β of a graph. We initiate a study on this parameter 2 ( ). it G γ We construct graphs for prescribed ( ) t G γ and 2 ( ). it G γ Also we determine bounds for 2 it γ value of graphs.
A subset S of vertices of a graph G with no isolated vertices is an independent semitotal dominat... more A subset S of vertices of a graph G with no isolated vertices is an independent semitotal dominating set if S is an independent dominating set, and for each u S there is a v S at a distance exactly two. The independent semitotal domination number of a graph is the minimum size of an independent semitotal dominating set of vertices in G and is denoted by γit2(G). This paper initiates the study of independent semitotal bondage number of graphs. The independent semitotal bondage number denoted by bit2(G), is the minimum number of edges whose removal from the graph increases the independent semitotal domination number.
A dominating set S of vertices of a graph G without isolated vertices is an independent semitotal... more A dominating set S of vertices of a graph G without isolated vertices is an independent semitotal dominating set if it is an independent dominating set and to each u in S there is a v in S at a distance exactly two. The independent semitotal domination number of a graph is the minimum size of an independent semitotal dominating set of vertices in G. In this paper, we have obtained the bounds for independent semitotal domination number in the Cartesian product of paths, path with a cycle and cycles.
A dominating set S of vertices of G without isolated vertices is an independent semitotal dominat... more A dominating set S of vertices of G without isolated vertices is an independent semitotal dominating set of G if S is an independent dominating set and to each u in S there is a v in S at a distance exactly two. The minimum and maximum cardinality of a minimal independent semitotal dominating set is called independent semitotal domination number and upper independent semitotal domination number of G, denoted by it2(G) and Γit2(G) respectively. The independent semitotal domination subdivision number sd it2(G) as the minimum number of edges to be subdivided (where no edge can be subdivided more than once) to increase the independent semitotal domination number. In this paper independent semitotal domination number and subdivision number with respect to this parameter of some special graphs are determined and studied.
International Journal of Mathematics Trends and Technology, Dec 29, 2023
A subset S of vertices of a graph G with no isolated vertices is an independent semitotal dominat... more A subset S of vertices of a graph G with no isolated vertices is an independent semitotal dominating set if S is an independent dominating set, and for each u S there is a v S at a distance exactly two. The independent semitotal domination number of a graph is the minimum size of an independent semitotal dominating set of vertices in G and is denoted by γit2(G). This paper initiates the study of independent semitotal bondage number of graphs. The independent semitotal bondage number denoted by bit2(G), is the minimum number of edges whose removal from the graph increases the independent semitotal domination number.
Journal of information & optimization sciences, 2024
In this paper a slight different parameter, independent semitotal domination number- This paramet... more In this paper a slight different parameter, independent semitotal domination number- This parameter lies between ( ) i G and 0 ( ) G β of a graph. We initiate a study on this parameter 2 ( ). it G γ We construct graphs for prescribed ( ) t G γ and 2 ( ). it G γ Also we determine bounds for 2 it γ value of graphs.
A subset S of vertices of a graph G with no isolated vertices is an independent semitotal dominat... more A subset S of vertices of a graph G with no isolated vertices is an independent semitotal dominating set if S is an independent dominating set, and for each u S there is a v S at a distance exactly two. The independent semitotal domination number of a graph is the minimum size of an independent semitotal dominating set of vertices in G and is denoted by γit2(G). This paper initiates the study of independent semitotal bondage number of graphs. The independent semitotal bondage number denoted by bit2(G), is the minimum number of edges whose removal from the graph increases the independent semitotal domination number.
Uploads
Papers by Sabari manju