分裂圖的(2, 1)-全標號

Abstract

A (p,1)-total labeling of a graph G is to be an assignment of integers to V(G)∪E(G)such that:(i)any two adjacent vertices of G receive distinct integers,(ii)any two adjacent edges of G receive distinct integers,and(iii)a vertex and its incident edge receive integers that differ by at least p in absolute value. The span of a (p,1)-total labeling is the maximum difference between two labels. The minimum span of a (p,1)-total labeling of a graph G is called the (p,1)-total number and denoted by λTp(G). Let G and H be two disjoint graphs. The join of G and H is the graph G∨H=(V,E),where V=V(G)∪V(H)and E=E(G)∪E(H)∪{(u,v)|u∈V(G),v∈V(H)}. Let Om be a graph with m vertices and no edges. Then we say the graph Om ∨ Kn to be a split graph. In this thesis, we mainly focus on the (2,1)-total labeling of split graph and we obtain some results about it.