Adjacent Vertex Reducible Edge Coloring of Splitting Graphs

Abstract

Ingraph theory, agraphG=(V,E) is labeled ashavinganadjacent vertexreducibleedgecoloring if there existsamappingf :E(G)→1,2,3,4...K,suchthatadjacent vertices u and v with the same degree generate sets s(u) ands(v) respectively,whereS(u)={f(uv)/uv∈E(g)}and S(u)=S(v).This studyfocusesoncalculatingthechromatic numberforadjacentvertexreducibleedgecoloringofsplitting graphs.