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Full-Text Articles in Physical Sciences and Mathematics
Linear Operators That Preserve Two Genera Of A Graph, Leroy B. Beasley, Kyung-Tae Kang, Seok-Zun Song
Linear Operators That Preserve Two Genera Of A Graph, Leroy B. Beasley, Kyung-Tae Kang, Seok-Zun Song
Mathematics and Statistics Faculty Publications
If a graph can be embedded in a smooth orientable surface of genus g without edge crossings and can not be embedded on one of genus g − 1 without edge crossings, then we say that the graph has genus g. We consider a mapping on the set of graphs with m vertices into itself. The mapping is called a linear operator if it preserves a union of graphs and it also preserves the empty graph. On the set of graphs with m vertices, we consider and investigate those linear operators which map graphs of genus g to graphs of …
Linear Operators That Preserve The Genus Of A Graph, Leroy B. Beasley, Jeong Han Kim, Seok-Zun Song
Linear Operators That Preserve The Genus Of A Graph, Leroy B. Beasley, Jeong Han Kim, Seok-Zun Song
Mathematics and Statistics Faculty Publications
A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus k−1. A mapping of the set of graphs on n vertices to itself is called a linear operator if the image of a union of graphs is the union of their images and if it maps the edgeless graph to the edgeless graph. We investigate linear operators on the set of graphs on n vertices that map graphs of genus k to graphs of genus k and graphs of genus k+1 to graphs …