a watching system in a graph $g=(v, e)$ is a set $w={omega_{1}, omega_{2}, cdots, omega_{k}}$, where $omega_{i}=(v_{i}, z_{i}), v_{i}in v$ and $z_{i}$ is a subset of closed neighborhood of $v_{i}$ such that the sets $l_{w}(v)={omega_{i}: vin omega_{i}}$ are non-empty and distinct, for any $vin v$. in this paper, we study the watching systems of line graph $k_{n}$ which is called triangular grap...

Code comments are the primary means to document implementation and facilitate program comprehension. Thus, their quality should be a concern improve maintenance. While much effort has been dedicated detecting bad smells, such as clones in code, little work focused on comments. In this paper we present our solution detect that developers fix. RepliComment can automatically analyze Java projects ...

OBJECTIVE To estimate the relationship between variations in medical spending and health outcomes of the elderly. DATA SOURCES 1992-2002 Medicare Current Beneficiary Surveys. STUDY DESIGN We used instrumental variable (IV) estimation to identify the relationships between alternative measures of elderly Medicare beneficiaries' medical spending over a 3-year observation period and health stat...

An identifying code in a graph is a subset of vertices having a nonempty and distinct intersection with the closed neighborhood of every vertex. We prove that the infimum density of any identifying code in Sk (an infinite strip of k rows in the square grid) can always be achieved by a periodic identifying code with pattern length at most 2. Assisted by a compute program implementing Karp’s algo...