Research On Some Properties Of Exchanged Folded Crossed Cube

Dominating problem on Graph has aroused great interest of scholars at home and abroad since it was first proposed,and many achievements have been made in recent decades.As a new type of interconnection network,the exchanged fold-ed crossed cube networks has good properties in many aspects.This article mainly discussed the exchanged folded crossed cube networks(EFCQ(s,t))and cartesian(EFCQ(s,t)× H)domination number,as well as other domination number of ex-changed folded crossed cube,including signed domination number,reverse signed domination number,total domination number and minus domination number.the last we discussed the properties of cycle of exchanged folded crossed cube.The main results were as follows:1.In this paper,there are mainly the following results about domination num-ber of exchanged folded crossed cube,which are:(1)when s=1,t?1,the specific values of domination number of EFCQ(s,t)is determined,And we are going to give a bound of domination number of EFCQ(s,s).(2)Haizhong Shi thinks that EFCQ(s,t)satisfies Vizing conjecture.In this paper,the bounds of domination num-ber of EFCQ(s,t)× H are determined.EFCQ(s,t)is EFCQ(1,1),EFCQ(1,2),EFCQ(2,2),EFCQ(1,t),H is K2,C3.And proved EFC,Q(1,1)satisfies Vizing conjecture.2.In this paper,other domination number of exchanged folded crossed cube mainly have the following results,which are:(1)when 1?s?2,1?t?3,the specific values of signed domination number of EFCQ(s,t)is determined.(2)the specific value of reverse signed domination number of EFCQ(1,1)is deter-mined,And we are going to give a bound of reverse signed domination number of EFCQ(2,2),EFCQ(3,3).(3)when 1 ?s ?2,1 ?t<3,the specific values of total domination number of EFCQ(s,t)is determined,and a bound of total domi-nation number of EFCQ(3,3)is determined.(4)this paper gives the specific value of minus domination number of EFCQ(1,1)and a bound of minus domination number of EFCQ(2,2).3.In this paper,there are mainly the following results about properties of the cycle of exchanged folded crossed cube,which are:(1)Haizhong Shi proposed follow-ing conjectures,conject,ures 1:EFCQ(s,s)is Hamilton decomposition;conjectures 2:EFCQ(2s,2s)is 2 factorable decomposition.This paper proves that the above conjecture is true,when s=1,2.(2)When s=1,2,3,4,This paper proves four basic properties of cycle of EFCQ(s,s).