Smarandachely Adjacent Vertex Distinguishing Edge Coloring Algorithm of Graphs

Abstract

To solve the problem of Smarandachely Adjacent Vertex Distinguishing Edge Coloring(SAVDEC) of graphs,this paper presents a coloring algorithm based on multi-objective optimization.For each sub problem,the sub objective function vector and decision space are set respectively.The optimal solution for sub objectives is gradually obtained during color iteration,sequential switching,and forced switching,making the total objective function meet the requirements of Smarandachely adjacent vertex distinguishing edge coloring ultimately.Experimental results show that,the proposed algorithm is able to get the number of colors for the Smarandachely adjacent vertex distinguishing edge of random graph within 1 000 vertices correctly.