No abstract

Chung and Liu have defined thed-chromatic Ramsey number as follows. Let1≤d≤cand lett=(cd). Let1,2,…,tbe the ordered subsets ofdcolors chosen fromcdistinct colors. LetG1,G2,…,Gtbe graphs. Thed-chromatic Ramsey number denoted byrdc(G1,G2,…,Gt)is defined as the least numberpsuch that, if the edges of the complete graphKpare colored in any fashion withccolors, then for somei, the subgraph whose edges are colored in theith subset of colors contains aGi. In this paper it is shown thatr23(Pi,Pj,Pk)=[(4k+2j+i−2)/6]wherei≤j≤k<r(Pi,Pj),r23stands for a generalized Ramsey number on a2-colored graph andPiis a path of orderi.

No abstract

Let G (V, E) be a graph with vertex set V and edge set E. The process of assigning natural numbers to the vertices of G such that the product of the numbers of adjacent vertices of G is a Zumkeller number on the edges of G is known as Zumkeller labeling of G. This can be achieved by defining an appropriate vertex function of G. In this article, we show the existence of this labeling to complete graph and fan graph.

No abstract