In the fractional graph colouring problem, the task is to schedule the activities of the nodes so that each node is active for 1 time unit in total, and at each point of time the set of active nodes forms an independent set. We show that for any α > 1 there exists a deterministic distributed algorithm that finds a fractional graph colouring of length at most α(∆ + 1) in any graph in one synchro...

In Graph Theory, independent number and, dominating number are three of the important parameters to measure the resilience of graphs, respectively denoted by ( ) G  and ( ) G  for a graph G . But predecessors have proved that computing them are very hard. So computing ( ) G  and ( ) G  of some particular known graphs is extremely valuable. In this paper, we determine ( ) G  and ( ) G  of ...

Let $kgeq 1$ be an integer, and let $G$ be a graph. A {it$k$-rainbow dominating function} (or a {it $k$-RDF}) of $G$ is afunction $f$ from the vertex set $V(G)$ to the family of all subsetsof ${1,2,ldots ,k}$ such that for every $vin V(G)$ with$f(v)=emptyset $, the condition $bigcup_{uinN_{G}(v)}f(u)={1,2,ldots,k}$ is fulfilled, where $N_{G}(v)$ isthe open neighborhood of $v$. The {it weight} o...

Olive grows in the mid-latitudes in the world and in areas with Mediterranean climate. Olive is one of the important agricultural products in Mediterranean Basin and Turkey. Its contribution to economy makes it valuable to determine the genetic relations among different olive varieties. In this study, genetic variations among 13 different olive cultivars were determined through 22 ISSR primers ...

‎A set of vertices $S$ of a graph $G$ is called a fixing set of $G$‎, ‎if only the trivial automorphism of $G$ fixes every vertex in $S$‎. ‎The fixing number of a graph is the smallest cardinality of a fixing‎ ‎set‎. ‎The fixed number of a graph $G$ is the minimum $k$‎, ‎such that ‎every $k$-set of vertices of $G$ is a fixing set of $G$‎. ‎A graph $G$‎ ‎is called a $k$-fixed graph‎, ‎if its fix...