A function f is called a Heronian Mean Labeling of a graph G = (V,E) with p vertices and q edges if it is possible to label the vertices Î with distinct labels () from 1,2,..,q+1 in such a way that when each edge = is labeled with (=) = ⌈ () + √ () () + () ⌉ () ⌊ () + √ () () + () ⌋ then the edge labels are distinct. In this case, f is a Heronian mean labeling of G and G is called a Heronian Mean Graph. In this paper, we prove that Path,

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We add to some fresh outcomes for Super Heronian Mean Labeling of graphs. It has been found that the graphs obtained by the collection of Triangular snake, Quadrilateral snake also admit Super Heronian Mean Labeling.

If each subgraph of the decomposition π of the graph G has the Steiner number same as G then π is said to be a Steiner decomposition of G. The maximum cardinality among the Steiner decomposition π of G is the Steiner decomposition number of G and is denoted by π st (G). In this paper, we present the Steiner decomposition number for Complete n-Sun graph.

Let f: V(G)  {1,2,…,p+q} be an injective function. For a vertex labeling "f" the induced edge labeling f* (e=uv) is defined by, f* (e) = ⌈√ () ()⌉ or ⌊√ () ()⌋.Then f is called a Super Geometric mean labeling if * (())+  * () ()+ = * +, A graph which admits Super Geometric mean labeling is called Super Geometric mean graph.