Abstract
Our objects are (2.1) to introduce the graphical concept of a circular caterpillar together with cyclical code of non-negative integers, and (2.2) to provide an elementary example of the simplest kind of application of the celebrated Polya Enumeration Theorem.
Highlights
In general we follow the notation and terminology of [1,4]
The characterization if that T 2 is hamiltonian if and only if T does not contain SK1,3, the subdivision graph of the star Kt,3 as a subtree. This criterion says that T is a caterpillar, a tree whose "pruned subtree" T' is a path, called its spine, P5
The end-degree ed( u) of a node u of tree T is the number of nodes of degree 1 adjacent to u
Summary
In general we follow the notation and terminology of [1,4]. The wellknown species of trees called caterpillars were first discovered [9] when 1 asked my doctoral student, Allen Schwenk, wich trees T have a Hamiltonian square. This criterion says that T is a caterpillar, a tree whose "pruned subtree" T' (obtained by deleting all the endnodes of T) is a path, called its spine, P5 We [10] derived a formula for the number of caterpillars with n nodes having given spine P5
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
