A dominating induced matching(DIM)of G is an induced matching that dominates every edge of G.In this note,we completely determine the number of DIMs in the generalized Petersen graph P(n,k).We prove that if P(n,k)is a...A dominating induced matching(DIM)of G is an induced matching that dominates every edge of G.In this note,we completely determine the number of DIMs in the generalized Petersen graph P(n,k).We prove that if P(n,k)is a generalized Petersen graph with n=0(mod 5)and k=2,3(mod 5),then E(P(n,k))can be partitioned into five DIMs.Meanwhile,in the left cases k=0,1,4(mod 5),we build some counterexamples to show that there exist some P(n,k)'s which are DIM-free.展开更多
基金Ming Chen was supported by National Key Research and Development Program of China(No.2024YFA1013900)。
文摘A dominating induced matching(DIM)of G is an induced matching that dominates every edge of G.In this note,we completely determine the number of DIMs in the generalized Petersen graph P(n,k).We prove that if P(n,k)is a generalized Petersen graph with n=0(mod 5)and k=2,3(mod 5),then E(P(n,k))can be partitioned into five DIMs.Meanwhile,in the left cases k=0,1,4(mod 5),we build some counterexamples to show that there exist some P(n,k)'s which are DIM-free.
