Sum signed graphs - I

Sum Signed Graphs – Ii

“…The motivation for the concept of sum signed labeling arose from the above idea that the vehicles passing through a road are sometimes restricted in terms of width of the road from a smooth, continuous ride. Introductory studies on sum signed graphs is available in [7]. In this paper, we extend the studies on sum signed graphs.…”

“…Definition 2 [7]. The smallest number of negative edges among all sum signed labeling of its underlying graph G is called the rna number.…”

“…Thus, there exists only one sum signed labeling of the graph. For n = 3, the number of negative edges in K 3 is 2 as given [7]. When n ≥ 4, the minimum size of cycle present in K n is that of 3.…”

“…The concept of rna number in parity signed graphs was introduced in [2] and was studied in [3]. In [7], the rna number of sum signed graphs was introduced and has been found for various types of graphs. Here, the concept will be generalized in particular for acyclic graphs.…”