Abstract
A labeling on a graph G with n vertices and m edges is called square sum if there exists a bijection f : V G ⟶ 0,1,2,3 , … , n − 1 such that the function f ∗ : E G ⟶ N defined by f ∗ s t = f s 2 + f t 2 , for all s t ∈ E G , is injective. A graph G having a square sum labeling is called square sum. In this study, we have investigated the square sum labeling of generalized Petersen graph and double generalized Petersen graph.
Highlights
In [1], Germina et al derived square sum labeling for basic graphs such as trees and cycles
In [1], Germina et al proved that the complete graph Kn is square sum iff n ≤ 7 and the other graphs which they proved to be square sum are trees, unicyclic graphs, mCn, and cycles’ chord; the graphs obtained by connected two copies of cycle Cn passes through the path Pk, a path union of k copies of Cn, and the path is P2
We have proved that the double generalized Petersen graph is a square sum graph for a particular case when k 1
Summary
In [1], Germina et al derived square sum labeling for basic graphs such as trees and cycles. E square sum labeling of edge xiyi, for i (n/2), is f∗ xiyi f xi2 + f yi2 E square sum labeling of the edges yiyi+1, for (n/2) + 1 ≤ i ≤ n − 2, is f∗ yiyi+1 f yi2 + f yi+12 n
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