For a graph G and an integer r ≥ 1, G is r-EKR if no intersecting family of independent r-sets of G is larger than the largest star （a family of independent r-sets containing some fixed vertex in G）, and G is stric...For a graph G and an integer r ≥ 1, G is r-EKR if no intersecting family of independent r-sets of G is larger than the largest star （a family of independent r-sets containing some fixed vertex in G）, and G is strictly r-EKR if every extremal intersecting family of independent r-sets is a star. Recently, Hurlbert and Kamat gave a preliminary result about EKR property of ladder graphs. They showed that a ladder graph with n rungs is 3-EKR for all n ≥3. The present paper proves that this graph is r-EKR for all 1 ≤ r 〈 n, and strictly r-EKR except for r = n - 1.展开更多
The notion of super-edge-graceful graphs was introduced by Mitchem and Simoson in 1994.However, few examples except trees are known. In this paper, we exhibit two classes of infinitely many cubic graphs which are supe...The notion of super-edge-graceful graphs was introduced by Mitchem and Simoson in 1994.However, few examples except trees are known. In this paper, we exhibit two classes of infinitely many cubic graphs which are super-edge-graceful. A conjecture is proposed.展开更多
基金Supported by the National Natural Science Foundation of China(No.11201409,No.11371327)the Natural Science Foundation of Hebei Province of China(No.A2013203009)
文摘For a graph G and an integer r ≥ 1, G is r-EKR if no intersecting family of independent r-sets of G is larger than the largest star （a family of independent r-sets containing some fixed vertex in G）, and G is strictly r-EKR if every extremal intersecting family of independent r-sets is a star. Recently, Hurlbert and Kamat gave a preliminary result about EKR property of ladder graphs. They showed that a ladder graph with n rungs is 3-EKR for all n ≥3. The present paper proves that this graph is r-EKR for all 1 ≤ r 〈 n, and strictly r-EKR except for r = n - 1.
基金Partially supported by Faculty-Research Grant,Hong Kong Baptist University
文摘The notion of super-edge-graceful graphs was introduced by Mitchem and Simoson in 1994.However, few examples except trees are known. In this paper, we exhibit two classes of infinitely many cubic graphs which are super-edge-graceful. A conjecture is proposed.
