(a) If we consider the intersections of the circle Hi(O) (center Hi and radius HiO) with the line Ai+1Ai+2, then we obtain six points which all lie on a circle with center H (first Droz-Farny circle). (b) If we consider the intersections of the circle Mi(H) (center Mi and radius MiH) with the line AiAi+1, then we obtain six points which all lie on a circle with center O (second Droz-Farny circl...

Maxillo-mandibular advancement MMA is considered an efficacious treatment for patients affected by severe obstructive sleep apnoea syndrome (OSAS). Even though OSAS improvement is the main goal of MMA, excessive maxillo-mandibular protrusion should be avoided to guarantee pleasant postoperative facial aesthetics. In order to attain such a result, the amount of MMA should be planned preoperative...

The Clustered Steiner tree problem is a variant of Steiner minimum tree problem. The required vertices are partitioned into clusters, and the subtrees spanning different clusters must be disjoint in a feasible clustered tree. In this paper we show that the Steiner ratio of the cluster Steiner tree problem is three, where the Steiner ratio is defined as the largest possible ratio of the minimal ...

In this paper we answer a question posed [1]. We show that χ(H2m,3m+2) = m + k + 1 such that k = m/2 and H2m,3m+2 is the Harary graph. Mathematics Subject Classification: 05C15

Given a graph G = (V, E) with a length function on edges and a subset R of V , the full Steiner tree is defined to be a Steiner tree in G with all the vertices of R as its leaves. Then the full Steiner tree problem is to find a full Steiner tree in G with minimum length, and the bottleneck full Steiner tree problem is to find a full Steiner tree T in G such that the length of the largest edge i...

In economics there is presently an almost revolutionary development. The direct measurement of subjective welfare challenges traditional economics, inspires B.S. Frey ( ) Warwick Business School, University of Warwick, Warwick, UK e-mail: [email protected] B.S. Frey Center for Research in Economics, Management and the Arts, Basel, Switzerland L. Steiner University of Zürich, Zürich, Switze...

We study an impartial game introduced by Anderson and Harary. This game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins. We determine the nimnumbers of this game for generalized dihedral groups, which are of the form Dih(A) = Z2 n A for a finite abelian group A.

We determine the minimum size of n-factor-critical graphs and that of k-extendable bipartite graphs, by considering Harary graphs and related graphs. Moreover, we determine the minimum size of k-extendable non-bipartite graphs for k = 1, 2, and pose a related conjecture for general k.

The Steiner connectivity problem is a generalization of the Steiner tree problem. It consists in finding a minimum cost set of simple paths to connect a subset of nodes in an undirected graph. We show that polyhedral and algorithmic results on the Steiner tree problem carry over to the Steiner connectivity problem; namely, the Steiner cut and the Steiner partition inequalities, as well as the a...

For a connected graph G, a set of vertices W in G is called a Steiner dominating set if W is both a Steiner set and a dominating set. The minimum cardinality of a Steiner dominating set of G is its Steiner domination numberand is denoted by ) (G s  . In this paper, it is studied that how the Steiner domination number is affected by adding a single edge to paths, complete graphs, cycles, star a...