论文标题
与边缘分离周期的图表的度量尺寸的界限
Bounds on metric dimensions of graphs with edge disjoint cycles
论文作者
论文摘要
在图G中，区分V（g）的每个元素的最小有序的顶点的基数是G（顶点）度量尺寸。同样，如果区分E（g），则该集合的基数是G的边缘度量尺寸。在本文中，这些不变符首先被认为是单环图的，并且表明顶点和边缘度量尺寸从两个特定的连续整数中获得值，这可以从图形的结构确定。因此，因此，我们得到这两个不变式在相同的单行图中最多可以有所不同。接下来，我们将结果扩展到具有边缘分离循环的图表，表明两个不变性最大都可以通过C差异，其中C是该图中的循环数。我们以一个猜想的方式结束了本文，该论文通过声称不变的差异仍然由c界定，从而概括了前面提到的带有规定的循环数字C的后果。
In a graph G, cardinality of the smallest ordered set of vertices that distinguishes every element of V (G) is the (vertex) metric dimension of G. Similarly, the cardinality of such a set is the edge metric dimension of G, if it distinguishes E(G). In this paper these invariants are considered first for unicyclic graphs, and it is shown that the vertex and edge metric dimensions obtain values from two particular consecutive integers, which can be determined from the structure of the graph. In particular, as a consequence, we obtain that these two invariants can differ for at most one for a same unicyclic graph. Next we extend the results to graphs with edge disjoint cycles showing that the two invariants can differ at most by c, where c is the number of cycles in such a graph. We conclude the paper with a conjecture that generalizes the previously mentioned consequences to graphs with prescribed cyclomatic number c by claiming that the difference of the invariant is still bounded by c.
