Let C_n^k be the kth power of cycle C_n. A set S of vertices of C_n^k is a monophonic vertex cover of C_n^k if S is both a monophonic set and a vertex cover of C_n^k. The minimum cardinality of a monophonic vertex cover of C_n^k is called the monophonic vertex covering number of power of cycles and is denoted by m_α(C_n^k). Any monophonic vertex cover of cardinality m_α(C_n^k) is a m_α-set of C_n^k. Some general properties satisfied by monophonic vertex cover of power of cycles are studied.

monophonic set, vertex covering set, monophonic vertex cover, monophonic vertex covering number, power of cycles, monophonic vertex covering number of power of cycles