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...

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...

Consider a graph G with |V (G)| = p and |E(G)| q let f : V (G) → {k, k + 1, 2, . − 1}} be an injective function. The induced edge labeling ∗ for vertex is defined by (e) all e uv ∈ E(G) bijective. If f(V (G)) ∪ {f E(G)} , 1}, then called k-super cube root mean labeling. such exists, graph. In this paper, I introduce prove the existence of to graphs viz., triangular snake Tn, double D(Tn), Quadr...

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 ...

In a recent paper, the authors gave combinatorial formulas for Laurent expansions of super λ -lengths in marked disk, generalizing Schiffler's T -path formula. present we give an alternate expression these terms double dimer covers on snake graphs. This generalizes Musiker, Schiffler, and Williams.

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...

An injective function f : V (G)→ {0, 1, 2, . . . , q} is an odd sum labeling if the induced edge labeling f∗ defined by f∗(uv) = f(u) + f(v), for all uv ∈ E(G), is bijective and f∗(E(G)) = {1, 3, 5, . . . , 2q − 1}. A graph is said to be an odd sum graph if it admits an odd sum labeling. In this paper, we have studied the odd sum property of the subdivision of the triangular snake, quadrilatera...