let $g=(v,e)$ be a connected graph. the eccentric connectivity index of $g$, $xi^{c}(g)$, is defined as $xi^{c}(g)=sum_{vin v(g)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. the eccentric distance sum of $g$ is defined as $xi^{d}(g)=sum_{vin v(g)}ec(v)d(v)$, where $d(v)=sum_{uin v(g)}d_{g}(u,v)$ and $d_{g}(u,v)$ is the distance between $u$ and $v$ ...

We show that the directed st-connectivity problem cannot be expressed in symmetric Datalog, a fragment of Datalog introduced in [5]. It was shown there that symmetric Datalog programs can be evaluated in logarithmic space and that this fragment of Datalog captures logspace when augmented with negation, and an auxiliary successor relation S together with two constant symbols for the smallest and...

Attention Deficit/Hyperactivity Disorder (ADHD) is a clinical syndrome characterized by an onset in early life. More than 65% of patients persist with manifestations of ADHD in adulthood. These symptoms may interfere in activities of daily-living, interpersonal relationships and professional and academic achievement. Nevertheless, the observation of an important group of adults with ADHD who do...

Background: Early diagnosis of patients in the early stages of Alzheimer's, known as mild cognitive impairment, is of great importance in the treatment of this disease. If a patient can be diagnosed at this stage, it is possible to treat or delay Alzheimer's disease. Resting-state functional magnetic resonance imaging (fMRI) is very common in the process of diagnosing Alzheimer's disease. In th...

In this work we study the problem of efficiently isolating witnesses for the complexity classes NL and LogCFL, which are two well-studied complexity classes contained in P. We prove that if there is a L/poly randomized procedure with success probability at least 2/3 for isolating an s-t path in a given directed graph with a source sink pair (s, t) then NL is contained in L/poly. By isolating a ...

In this paper, we obtain the upper and lower bounds on the eccen- tricity connectivity index of unicyclic graphs with perfect matchings. Also we give some lower bounds on the eccentric connectivity index of unicyclic graphs with given matching numbers.