406,447 research outputs found
A Jenkins-Serrin problem on the strip
We describe the family of minimal graphs on strips with boundary values
disposed alternately on edges of length one, and whose conjugate
graphs are contained in horizontal slabs of width one in . We can
obtain as limits of such graphs the helicoid, all the doubly periodic Scherk
minimal surfaces and the singly periodic Scherk minimal surface of angle
A note on minimal matching covered graphs
A graph is called matching covered if for its every edge there is a maximum
matching containing it. It is shown that minimal matching covered graphs
contain a perfect matching.Comment: 4 page
The Minimal Total Irregularity of Graphs
In \cite{2012a}, Abdo and Dimitov defined the total irregularity of a graph
as
\hskip3.3cm
\noindent where denotes the vertex degree of a vertex . In
this paper, we investigate the minimal total irregularity of the connected
graphs, determine the minimal, the second minimal, the third minimal total
irregularity of trees, unicyclic graphs, bicyclic graphs on vertices, and
propose an open problem for further research.Comment: 13 pages, 4 figure
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