Unrooted binary tree enumeration problem on unrooted binary trees is to count the number of trees with "n" labeled leaves and unlabeled internal nodes. An unrooted binary tree on "n" labeled leaves can be formed by connecting the "n"th leaf to a new node in the middle of any of the edges of an unrooted binary tree on "n" − 1 labeled leaves. There are 2"n" − 5 edges at which the "n"th node can be attached; therefore, the number of trees on "n" leaves is larger than the number of trees on "n" − 1 leaves by a factor of 2"n" −
Contact binary of years, the common envelope is a dynamically unstable phase in binary evolution that either expels the stellar envelope or merges the binary in a timescale of months to years. Contact binary In astronomy, a contact binary is a binary star system whose component stars are so close that they touch each other or have merged to share their gaseous envelopes. A binary system whose stars share an envelope may also be called an overcontact binary. Almost all known contact binary systems are eclipsing binaries; eclipsing contact binaries are known as W Ursae Majoris variables, after their type star, W