Abstract
A chord of a path P is an edge joining two non-adjacent vertices of P. A path P is called a monophonic path if it is a chordless path. A monophonic graphoidal cover of a graph G is a collection m of monophonic paths in G such that every vertex of G is an internal vertex of at most one monophonic path in m and every edge of G is in exactly one monophonic path in m. The minimum cardinality of a monophonic graphoidal cover of G is called the monophonic graphoidal covering number of G and is denoted bym. We determine bounds for it and characterize graphs which realize these bounds. Also, for any positive integer n with q −p + 2 ≤ n ≤ q − 1, there exists a tree T such that the monophonic graphoidal covering number is n.
Sign-in/Register to access full text options 
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 callMore From: International Journal of Pure and Apllied Mathematics
Disclaimer: 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.
