For a nontrivial connected graph G with no isolated vertex, nonempty subset D \(\subseteq\) V (G) is rings dominating set if and for each vertex \(\upsilon\) \(\in\) \ adjacent to at least two vertices in D. Thus, the of all D, \(\mid\)N(\(\upsilon\)) \(\cap\) (V D)\(\mid\) \(\ge\) 2. Moreover, called minimum smallest size given graph. The cardinality domination number G, denoted by \(\gamma\)r...

A graph is said to be total-colored if all the edges and vertices of are colored. path in a total proper (i) any two adjacent on differ color, (ii) internal (iii) vertex differs color from its incident path. called total-proper connected by graph. For [Formula: see text], connection number denoted defined as smallest colors required make text] connected. In this paper, we study for operations. ...

Let G=(V,E) be a graph; set D⊆V is total dominating if every vertex v∈V has, at least, one neighbor in D. The domination number γt(G) the minimum cardinality among all sets. Given an arbitrary graph G, we consider some operators on this S(G),R(G), and Q(G), give bounds or exact value of these new graphs using parameters original G.

Fuzzy total chromatic number is the least value of k such that k-fuzzy coloring exist. In this paper, we discussed concept graphs to bistar graph and helm graph. Here define fuzzy Bistar Helm