Vertex Equitable Labeling of Double Alternate Snake Graphs

Authors

  • A. Maheswari 2Department of Mathematics, Kamaraj College of Engineering and Technology, Virudhunagar, India
  • M. Vijayalakshmi 3Department of Mathematics, Dr.G.U. Pope College of Engineering, Sawyerpuram, Thoothukudi District, Tamilnadu, India
  • P. Jeyanthi 1Research Center, Department of Mathematics, Govindammal Aditanar College for women, Tiruchendur - 628 215, Tamilnadu,India
Abstract:

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 induced edge labels are 1, 2, 3, . . . , q. In this paper, we prove that DA(Tn)⊙K1, DA(Tn)⊙2K1(DA(Tn) denote double alternate triangular snake) and DA(Qn) ⊙ K1, DA(Qn) ⊙ 2K1(DA(Qn) denote double alternate quadrilateral snake) are vertex equitable graphs.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

vertex equitable labeling of double alternate snake graphs

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...

full text

Equitable vertex arboricity of graphs

An equitable (t, k, d)-tree-coloring of a graph G is a coloring to vertices of G such that the sizes of any two color classes differ by at most one and the subgraph induced by each color class is a forest of maximum degree at most k and diameter at most d. The minimum t such that G has an equitable (t′, k, d)-tree-coloring for every t′ ≥ t is called the strong equitable (k, d)-vertex-arboricity...

full text

Some Results on Vertex Equitable Labeling

Let G be a graph with p vertices and q edges and let = 0,1, 2, , . 2 q A              A vertex labeling   : f V G A  i e a vertex equitable labeling of G if it induces an edge labeling s said to b given by      * =  f uv f u f v  * f such that     1 v a v b   and     * = 1,2,3, , f f f E q  , where   f v a is the ber of verti num ces v with   = f v a for . ...

full text

Equitable vertex arboricity of planar graphs

Let G1 be a planar graph such that all cycles of length at most 4 are independent and let G2 be a planar graph without 3-cycles and adjacent 4-cycles. It is proved that the set of vertices of G1 and G2 can be equitably partitioned into t subsets for every t ≥ 3 so that each subset induces a forest. These results partially confirm a conjecture of Wu, Zhang

full text

3-Equitable Prime Cordial Labeling of Graphs

A 3-equitable prime cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, ..., |V |} such that if an edge uv is assigned the label 1 if gcd(f(u), f(v)) = 1 and gcd(f(u) + f(v), f(u)−f(v)) = 1, the label 2 if gcd(f(u), f(v)) = 1 and gcd(f(u) + f(v), f(u)− f(v)) = 2 and 0 otherwise, then the number of edges labeled with i and the number of edges labeled with j differ b...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 46  issue 1

pages  27- 34

publication date 2016-01-07

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023