Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The resolving number of a graph   We study a graph parameter related to resolving sets and metric dimension,
namely the resolving number, introduced by Chartrand, Poisson and Zhang. First,
we establish an important difference between the two parameters: while
computing the metric dimension of an arbitrary graph is known to be NP-hard, we
show that the resolving number can be computed in polynomial time. We then
relate the resolving number to classical graph parameters: diameter, girth,
clique number, order and maximum degree. With these relations in hand, we
characterize the graphs with resolving number 3 extending other studies that
provide characterizations for smaller resolving number.

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The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph