Additively graceful signed graphs

Abstract

Let S = ( V , E , σ ) be a signed graph of order p and size q. Let E + : { e ∈ E : σ ( e ) = + } , E − = { e ∈ E : σ ( e ) = − } , | E + | = m and | E − | = n . Let f : V → { 0 , 1 , 2 , … + ⌈ n + 1 2 ⌉ } be an injective function and let g f ( u v ) = { | f ( u ) − f ( v ) | if u v ∈ E + f ( u ) + f ( v ) if u v ∈ E − The function f is called an additively graceful labeling of S if g f ( E + ) = { 1 , 2 , … , m } and g f ( E − ) = { 1 , 2 , … , n } . In this paper we investigate the existence of additively graceful labeling of several classes of signed graphs.