On Algorithms for Adjacent Vertex Distinguishing I-Total Coloring of Random Graphs

Key words: 
• random graph，algorithm，adjacent vertex distinguishing I-total coloring，adjacent vertex dis-tinguishing I-total chromatic number /
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Abstract: A random graphs is said to be adjacent vertex distinguishing I‐total coloring if the color of two adjacent vertexs ,adjacent edges and the color set of adjacent vertex w hich formed by the association edge color are different .Meanwhile ,the minimum number of colors is called the adjacent vertex distinguishing I‐total chromatic number w hich can be compute through a new heuristic intelligent algorithm that this pa‐per proposed .This algorithm according to adjacent vertex distinguishing I‐total coloring conditions to es‐tablish three subfunction and a main function ,using the exchange rule gradually search the optimum solu‐tion ,until when the value of main function fulfill the end requirement .This paper gives detailed design steps of the algorithm ,meanwhile tested and analyzed it .The test results show that this algorithm can cal‐culate adjacent distinguishing I‐total chromatic number of a graph w hich has definitized vertex number quickly and efficiently .The time complexity of this algorithm is less than O(n3 ) .