Circular layouts are a popular graph drawing style, where vertices are placed on a circle and edges are drawn as straight chords. Crossing minimization in circular layouts is NP-hard. One way to allow for fewer crossings in practice are two-sided layouts that draw some edges as curves in the exterior of the circle. In fact, oneand two-sided circular layouts are equivalent to one-page and two-pa...

We propose a new graph metric and study its properties. In contrast to the standard distance in connected graphs [5], it takes into account all paths between vertices. Formally, it is defined as d(i, j) = qii+qjj−qij−qji [11], where qij is the (i, j)-entry of the relative forest accessibility matrix Q(ε) = (I + εL)−1, L is the Laplacian matrix of the (weighted) (multi)graph, and ε is a positive...

A graph G is a Unit Disk (UD) graph if there is an assignment of unit disks centered at its vertices such that there is an edge in G iff the corresponding unit disks intersect. The square G of G is defined as a graph on the same vertex set as G and having edges between pairs of vertices with graph distance at most two in G. Our results on the chromatic number of G are motivated by an applicatio...

background & aim: healthcare areas, especially fertility care (commonly accompanied with high emotions, as well as long-term and recurring treatment periods) could exclusively benefit from patient-centered care (pcc). despite evident advantages of pcc, this approach has not been practiced as a routine procedure in current clinical environments yet, even in western developed countries. therefore...

The center and the periphery of a graph is the set of vertices with minimum resp. maximum eccentricity in it. A graph is almost self-centered (ASC) if it contains exactly two non-central vertices and is almost peripheral (AP) if all its vertices but one lie in the periphery. Answering a question from (Taiwanese J. Math. 18 (2014), 463–471) it is proved that for any integer r ≥ 1 there exists an...

We propose a new graph metric and study its properties. In contrast to the standard distance in connected graphs [5], it takes into account all paths between vertices. Formally, it is defined as d(i, j) = qii+qjj−qij−qji [11], where qij is the (i, j)-entry of the relative forest accessibility matrix Q(ε) = (I + εL)−1, L is the Laplacian matrix of the (weighted) (multi)graph, and ε is a positive...

let $r$ be a ring with unity. the undirected nilpotent graph of $r$, denoted by $gamma_n(r)$, is a graph with vertex set ~$z_n(r)^* = {0neq x in r | xy in n(r) for some y in r^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in n(r)$, or equivalently, $yx in n(r)$, where $n(r)$ denoted the nilpotent elements of $r$. recently, it has been proved that if $r$ is a left ar...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

background and purpose: various approaches to learning are suggested & practiced. the traditional medical education were more teacher centered oriented . in this method the students’ involvement in the process of learning is not remarkable, but the new approach to medical education supports the students involvement. this study evaluated the various method of lecturing considering students invol...