منابع مشابه
Uniquely pairable graphs
The concept of a k-pairable graph was introduced by Chen (On k-pairable graphs, Discrete Mathematics 287 (2004), 11–15) as an extension of hypercubes and graphs with an antipodal isomorphism. In this talk, we introduce a special class of k-pairable graphs which are called uniquely pairable graphs. Then we give a characterization of uniquely pairable graphs in terms of the prime factor decomposi...
متن کاملSolis Graphs and Uniquely Metric Basis Graphs
A set $Wsubset V (G)$ is called a resolving set, if for every two distinct vertices $u, v in V (G)$ there exists $win W$ such that $d(u,w) not = d(v,w)$, where $d(x, y)$ is the distance between the vertices $x$ and $y$. A resolving set for $G$ with minimum cardinality is called a metric basis. A graph with a unique metric basis is called a uniquely dimensional graph. In this paper, we establish...
متن کاملPath-pairable Graphs
A graph of even order is called path-pairable, if for any pairing of its vertices, there exist edge disjoint paths connecting the paired vertices. Extrernal problerns for path-pairable graphs with restrictions on the maxirnurn degree will be considered. In particular, let f(n, k) denote the rninirrnun nurnber of edges in a path-pair able graph of order nand rnaxirnum degree k. Exact values of j...
متن کاملSharp bounds on the size of pairable graphs and pairable bipartite graphs
The k-pairable graphs, introduced by Chen in 2004, constitute a wide class of graphs with a new type of symmetry, which includes many graphs of theoretical and practical importance, such as hypercubes, Hamming graphs of even order, antipodal graphs (also called diametrical graphs, or symmetrically even graphs), S-graphs, etc. Let k be a positive integer. A connected graph G is said to be k-pair...
متن کاملThree-regular path pairable graphs
A graph G with at least 2k vertices is k-path pairable if for any k pairs of distinct vertices 9f G there are k edge disjoint paths between the pairs. It will be shown for any positive integer k that there is a k-path pairable graph of maximum degree three.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.11.029