In this article,we obtain an upper bound for the regularity of the binomial edge ideal of a graph whose every block is either a cycle or a clique.As a consequence,we obtain an upper bound for the regularity of binomia...In this article,we obtain an upper bound for the regularity of the binomial edge ideal of a graph whose every block is either a cycle or a clique.As a consequence,we obtain an upper bound for the regularity of binomial edge ideal of a cactus graph.We also identify a certain subclass attaining the upper bound.展开更多
The distance between two vertices u and v in a connected graph G is the number of edges lying in a shortest path(geodesic)between them.A vertex x of G performs the metric identification for a pair(u,v)of vertices in G...The distance between two vertices u and v in a connected graph G is the number of edges lying in a shortest path(geodesic)between them.A vertex x of G performs the metric identification for a pair(u,v)of vertices in G if and only if the equality between the distances of u and v with x implies that u=v(That is,the distance between u and x is different from the distance between v and x).The minimum number of vertices performing the metric identification for every pair of vertices in G defines themetric dimension of G.In this paper,we performthemetric identification of vertices in two types of polygonal cacti:chain polygonal cactus and star polygonal cactus.展开更多
文摘In this article,we obtain an upper bound for the regularity of the binomial edge ideal of a graph whose every block is either a cycle or a clique.As a consequence,we obtain an upper bound for the regularity of binomial edge ideal of a cactus graph.We also identify a certain subclass attaining the upper bound.
文摘The distance between two vertices u and v in a connected graph G is the number of edges lying in a shortest path(geodesic)between them.A vertex x of G performs the metric identification for a pair(u,v)of vertices in G if and only if the equality between the distances of u and v with x implies that u=v(That is,the distance between u and x is different from the distance between v and x).The minimum number of vertices performing the metric identification for every pair of vertices in G defines themetric dimension of G.In this paper,we performthemetric identification of vertices in two types of polygonal cacti:chain polygonal cactus and star polygonal cactus.
