Uniquely pairable graphs
نویسنده
چکیده
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 decomposition.
منابع مشابه
Sharp 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 کاملNote on the diameter of path-pairable graphs
A graph on 2k vertices is path-pairable if for any pairing of the vertices the pairs can be joined by edge-disjoint paths. The so far known families of path-pairable graphs have diameter of atmost 3. In this paperwe present an infinite family of path-pairable graphswith diameter d(G) = O( √ n) where n denotes the number of vertices of the graph. We prove that our example is extremal up to a con...
متن کاملOn the maximum diameter of path-pairable graphs
A graph is path-pairable if for any pairing of its vertices there exist edge disjoint paths joining the vertices in each pair. We obtain sharp bounds on the maximum possible diameter of path-pairable graphs which either have a given number of edges, or are cdegenerate. Along the way we show that a large family of graphs obtained by blowing up a path is path-pairable, which may be of independent...
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.
متن کاملOn the maximum degree of path-pairable planar graphs
A graph is path-pairable if for any pairing of its vertices there exist edge-disjoint paths joining the vertices in each pair. We investigate the behaviour of the maximum degree in path-pairable planar graphs. We show that any n-vertex path-pairable planar graph must contain a vertex of degree linear in n.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 308 شماره
صفحات -
تاریخ انتشار 2008