I Wayan Sudarsana

THE RAMSEY NUMBER FOR A LINEAR FOREST VERSUS TWO IDENTICAL COPIES OF COMPLETE GRAPHS

Let H be a graph with the chromatic number h and the chromatic surplus s. A connected graph G of order n is called H-good if R(G, H) = (n - 1)(h - 1) + s. In this paper, we show that Pn is 2Km-good for n ≥ 3. Furthermore, we obtain the Ramsey number R(L, 2Km), where L is a linear forest. Moreover, we also give the Ramsey number R(L, Hm) which is an extension for R(kPn, Hm) proposed by Ali et al. [1], where Hm is a cocktail party graph on 2m vertices.

On Super Mean Labeling for Total Graph of Path and Cycle

Let be a graph with the vertex set and the edge set , respectively. By a graph we mean a finite undirected graph with neither loops nor multiple edges. The number of vertices of is called order of and it is denoted by . Let be a graph. A super mean graph on is an injection such that, for each edge in labeled by , the set forms . A graph which admits super mean labeling is called super mean graph. The total graph of is the graph with the vertex set and two vertices are adjacent whenever they are either adjacent or incident in . We have showed that graphs and are super mean, where is a path on vertices and is a cycle on vertices.

PELABELAN TOTAL SISI ANTI AJAIB SUPER (PTSAAS) PADA GABUNGAN GRAF BINTANG GANDA DAN LINTASAN

PELABELAN TOTAL SISI ANTI AJAIB SUPER (PTSAAS) PADA GABUNGAN GRAF BINTANG GANDA DAN LINTASAN