A Dimension 6 Graph with Minimum Edge-set
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DOI: 10.1007/s00373-017-1854-8
Abstract: The dimension of a graph G is defined to be the minimum n such that G has a representation as a unit-distance graph in $${{\mathbb {R}}}^n$$Rn. In this article, we show that a dimension 6… read more here.
Keywords: minimum edge; graph minimum; graph; dimension graph ... See more keywords
A Bound on the Number of Leaves in a Spanning Tree of a Connected Graph of Minimum Degree 6
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DOI: 10.1007/s10958-018-4132-2
Abstract: We prove that a connected graph of minimum degree 6 has a spanning tree such that at least 1121$$ \frac{11\ }{21} $$ of its vertices are leaves. read more here.
Keywords: bound number; graph minimum; connected graph; minimum degree ... See more keywords
Characterizing Forbidden Pairs for the Edge-Connectivity of a Connected Graph to Be Its Minimum Degree
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DOI: 10.3390/axioms11050219
Abstract: Let H be a class of given graphs. A graph G is said to be H-free if G contains no induced copies of H for any H∈H. In this article, we characterize all connected subgraph… read more here.
Keywords: minimum degree; connectivity connected; edge connectivity; characterizing forbidden ... See more keywords