Ladder and Subdivision of Ladder Graphs with Pendant Edges are Odd Graceful

Ladder and Subdivision of Ladder Graphs with Pendant Edges are Odd Graceful

The ladder graph plays an important role in many applications as Electronics, Electrical and Wireless communication areas. The aim of this work is to present a new class of odd graceful labeling for the ladder graph. In particular, we show that the ladder graph Ln with m-pendant Ln mk1 is odd graceful. We also show that the subdivision of ladder graph Ln with m-pendant S(Ln)  mk1 is odd grace...

Graceful graphs with pendant edges

Crown graphs and subdivision of ladders are odd graceful

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The birank number of ladder, prism and Mobius ladder graphs

Given a graph G, a function f : V (G)→ {1, 2, ..., k} is a k-biranking of G if f(u) = f(v) implies every u-v path contains vertices x and y such that f(x) > f(u) and f(y) < f(u). The birank number of a graph, denoted bi(G), is the minimum k such that G has a k-biranking. In this paper we determine the birank numbers for ladder, prism, and Möbius ladder graphs.

Further results on odd mean labeling of some subdivision graphs

Let G(V,E) be a graph with p vertices and q edges. A graph G is said to have an odd mean labeling if there exists a function f : V (G) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : E(G) → {1, 3, 5,...,2q - 1} defined by f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd is a bijection. A graph that admits an odd mean labelin...