Tree Domination Number of Semi Total Point Graphs

Objectives: The main aim of the research work is to study the concept of a tree domination number of semi-total point graphs. Method: A set D of a graph G = (V, E) is a dominating set, if every vertex in V- D is adjacent to at least one vertex in D. The domination number is the minimum cardinality of a dominating set D. A dominating set D is called a tree dominating set, if the induced subgraph is a tree. The minimum cardinality of a tree dominating set is called the tree-domination number of G and is denoted by . For any graph G = (V, E), the semi-total point graph T2(G) = H is the graph whose vertex set is the union of vertices and edges in which two vertices are adjacent if and only if they are adjacent vertices of G or one is a vertex and other is an edge of G incident with it. Findings: The characterizations of tree dominating set in semi total point graph sets to be minimal are found. To obtain the exact values, lower and upper bounds of tree dominating set in semi total point graph in some standard graphs. Novelty: This study provides bounds and results concerning the tree domination number of the semi-total point graph. This implies that the study likely presents new findings or insights into the behavior of these graphs. Keywords: Dominating set, Domination number, Tree dominating set, Tree domination number, Semi total point graph