Abstract
An arc of a graph is an oriented edge and a 3-arc is a 4-tuple ( v , u , x , y ) of vertices such that both ( v , u , x ) and ( u , x , y ) are paths of length two. The 3-arc graph of a graph G is defined to have the arcs of G as vertices such that two arcs u v , x y are adjacent if and only if ( v , u , x , y ) is a 3-arc of G . In this paper, we study the independence, domination and chromatic numbers of 3-arc graphs and obtain sharp lower and upper bounds for them. We introduce a new notion of arc-coloring of a graph in studying vertex-colorings of 3-arc graphs.
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.
