Microsoft Word - THE PERMUTATIONS ALGORITHM TO SOLVE THE GRAPH ISOMORPHISM.doc

THE PERMUTATIONS ALGORITHM TO SOLVE THE GRAPH +ISOMORPHISM *Hameed.H.Hameed Abstract This research study the isomorphism problem of two simple planar graphs which they have the same number of vertices and edges, we used the permutations algorithm which generates a permutation from known permutation. In this paper a program in (Mat Lab) has been constructed to compare two graphs by generating all permutations of the vertices of the first graph and finding the adjacency matrix of it in each permutation then compare it with the adjacency matrix of the second graph . Finally the result discuses whether the two graphs are isomorphic or not. : ﺹﻠﺨﺘﺴﻤﻝﺍ ﻥـﻋ ﻙـﻝﺫﻭ ﺕﺎﻓﺎﺤﻝﺍ ﻥﻤ ﺩﺩﻌﻝﺍ ﺱﻔﻨﻭ ﺱﻭﺅﺭﻝﺍ ﻥﻤ ﺩﺩﻌﻝﺍ ﺱﻔﻨ ﺎﻤﻬﻝ ﻥﻴﻴﻭﺘﺴﻤ ﻥﻴﻨﺎﻴﺒ لﻜﺎﺸﺘ ﺔﺴﺍﺭﺩﺒ ﺙﺤﺒﻝﺍ ﺍﺫﻫ ﻡﻭﻘﻴ ﺔﻁﺴﺍﻭﺒ ﺞﻤﺎﻨﺭﺒ ﺀﺎﺸﻨﺈﺒ ﺎﻨﻤﻗ ﺙﻴﺤ ،ﺎﹰﻘﺒﺴﻤ ﻰﻁﻌﻤ لﻴﺩﺒﺘ ﻥﻤ لﻴﺩﺒﺘ ﺩﻝﻭﺘ ﻲﺘﻝﺍﻭ لﻴﺩﺎﺒﺘﻝﺍ ﺔﻴﻤﺯﺭﺍﻭﺨ ﻡﺍﺩﺨﺘﺴﺍ ﻕﻴﺭﻁ ﺱﻭﺅﺭ لﻴﺩﺎﺒﺘ ﻥﻤ ﺔﺠﺘﻨﺘﺴﻤﻝﺍ ﺭﻭﺎﺠﺘﻝﺍ ﺕﺎﻓﻭﻔﺼﻤ لﻜ ﻊﻤ ﻥﻴﻨﺎﻴﺒﻝﺍ ﺩﺤﻷ ﺭﻭﺎﺠﺘﻝﺍ ﺔﻓﻭﻔﺼﻤ ﺔﻨﺭﺎﻘﻤﺒ ﻡﻭﻘﻴ (Mat Lab) ﻱﻭﺎﺴـﺘﻝﺍ ﻰﻠﻋ لﻭﺼﺤﻝﺍ ﻡﺩﻋ ﺩﻨﻋﻭ ﻥﻴﻠﻜﺎﺸﺘﻤ ﻥﻴﻨﺎﻴﺒﻝﺍ ﻥ ﻭﻜﻴ لﻴﺩﺎﺒﺘﻝﺍ ﺩﺤﺍ ﻲﻓ ﻥﻴﺘﻓﻭﻔﺼﻤﻝﺍ ﺕﻭﺎﺴﺘ ﺍﺫﺈﻓ ، ﺭﺨﻵﺍ ﻥﺎﻴﺒﻝﺍ .