Abstract
Let G be a (p,q) graph. An injective map f:V(G)→﹛±1,±2,...±p﹜is called a pair sum labeling if the induced edge function, fe:E(G)→Z-﹛0﹜defined by fe(uv)=f(u)+f(v) is one-one and fe(E(G)) is either of the form {±k1,±k2,...,±kq/2} or {±k1,±k2,...,±kq-1/2}∪{kq+1/2} according as q is even or odd. A graph with a pair sum labeling is called a pair sum graph. In this paper we investigate the pair sum labeling behavior of some trees which are derived from stars and bistars. Finally, we show that all trees of order nine are pair sum graphs.
Highlights
The graphs in this paper are finite, undirected and simple.V G and E G will denote the vertex set and edge set of a graph G
In this paper we investigate the pair sum labeling behavior of some trees which are derived from stars and bistars
We show that all trees of order nine are pair sum graphs
Summary
The graphs in this paper are finite, undirected and simple. V G and E G will denote the vertex set and edge set of a graph G. The cardinality of the vertex set of a graph G is called the order of G and is denoted by p. The cardinality of its edge set is called the size of G and is denoted by q. The concept of pair sum labeling has been introduced in[1].The Pair sum labeling behavior of some standard graphs like complete graph, cycle, path, bistar, and some more standard graphs are investigated in [1,2,3]. We proved that all trees of order nine are pair sum. X stands for the largest integer less than or equal to x and x stands for the smallest inter greater than or equal to x
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