let g be a graph with p vertices and q edges and a = {0, 1, 2, . . . , [q/2]}. a vertex labeling f : v (g) → a induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. for a ∈ a, let vf (a) be the number of vertices v with f(v) = a. a graph g is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in a, |vf (a) − vf (b)| ≤ 1 and the in...

Abstract: A graph G with p vertices is said to be strongly multiplicative if the vertices of G can be labeled with p consecutive positive integers 1, 2, ..., p such that label induced on the edges by the product of labels of end vertices are all distinct. In this paper we investigate strongly multiplicative labeling of some snake related graphs. We prove that alternate triangular snake and alte...

An injective map f : E(G) → {±1,±2, · · · ,±q} is said to be an edge pair sum labeling of a graph G(p, q) if the induced vertex function f∗ : V (G) → Z − {0} defined by f∗(v) = ∑ e∈Ev f (e) is one-one, where Ev denotes the set of edges in G that are incident with a vetex v and f∗(V (G)) is either of the form { ±k1,±k2, · · · ,±k p 2 } or { ±k1,±k2, · · · ,±k p−1 2 } ∪ { ±k p+1 2 } according as ...

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defi ned by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

Our paper has two goals: i) We propose the combinatorial approach to facilitate the calculation of the number of spanning trees for five new classes of graphs. ii) We use a new powerful operation (subdivision) to get larger graphs from a given graph. In particular, we derive the explicit formulas for the subdivision of ladder, fan, triangular snake, double triangular snake and the total graph o...

Let G be a graph with p vertices and q edges and A = {0, 1, 2, . . . , [q/2]}. A vertex labeling f : V (G) → A induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. For a ∈ A, let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, |vf (a) − vf (b)| ≤ 1 and the indu...

A graph G= (V,E) with p vertices and q edges is called a Harmonic mean graph if it is possible to label the vertices xV with distinct labels f(x) from 1,2,....,q+1 in such a way that when each edge e=uv is labeled with f(uv)= ( ) ( ) ( ) ( ) (or) ( ) ( ) ( ) ( ) , then the edge labels are distinct. In this case, f is called Harmonic mean labeling of G. In this paper we prove that Double Triang...

The aim of this paper is to present some odd graceful graphs. In particular we show that an odd graceful labeling of the all subdivision of double triangular snakes ( 2 k ∆ -snake ). We also prove that the all subdivision of 2 1 m∆ -snake are odd graceful. Finally, we generalize the above two results (the all subdivision of 2 k m∆ -snake are odd graceful).

The adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for a G, in which no two vertices are incident to edges colored with same set colors. an G called edge-chromatic index. In this paper, I compute index Anti-prism, sunflower graph, double triangular winged prism, rectangular prism and Polygonal snake graph.

We introduce new labeling called m-bonacci graceful labeling. A graph G on n edges is if the vertices can be labeled with distinct integers from set {0,1,2,…,Zn,m} such that derived edge labels are first numbers. show complete graphs, bipartite gear triangular grid and wheel graphs not graceful. Almost all trees give to cycles, friendship polygonal snake double graphs.