Switching is a local transformation that when applied to a combinatorial object gives another object with the same parameters. It is here shown that the cycle switching graph of the 11 084 874 829 isomorphism classes of Steiner triple systems of order 19 as well as the cycle switching graph of the 1 348 410 350 618 155 344 199 680 000 labeled such designs are connected. In addition to giving an...

We investigate the conditions under which a Steiner triple system can have a 2or 3-existentially closed block intersection graph.

An emanation graph of grade k on a set points is plane spanner made by shooting $$2^{k+1}$$ equally spaced rays from each point, where the shorter stop longer ones upon collision. The collision are Steiner spanner. Emanation graphs one were studied Mondal and Nachmanson in context network visualization. They proved that spanning ratio such bounded $$(2+\sqrt{2})\approx 3.414$$ . We improve this...

the wiener polarity index wp(g) of a molecular graph g of order n is the number ofunordered pairs of vertices u, v of g such that the distance d(u,v) between u and v is 3. in anearlier paper, some extremal properties of this graph invariant in the class of catacondensedhexagonal systems and fullerene graphs were investigated. in this paper, some new bounds forthis graph invariant are presented....

The Steiner tree problem asks for a shortest subgraph connecting a given set of terminals in a graph. It is known to be APX-complete, which means that no polynomial time approximation scheme can exist for this problem, unless P=NP. Currently, the best approximation algorithm for the Steiner tree problem has a performance ratio of + , , whereas the corresponding lower bound is smaller than + , ....

Given a complete graph G = (V,E) with a metric cost function c : E → R and two vertex subsets R ⊂ V and R ⊆ R, a partial-terminal Steiner tree is a Steiner tree which contains all the vertices in R such that all the vertices in R are leaves. The partial-terminal Steiner tree problem (PTSTP) is to find a partial-terminal Steiner tree with the minimum cost. The problem has been shown to be NP-har...

In a Steiner triple system STS(v)=(V,B), for each pair {a, b} ⊂ V , the cycle graph Ga,b can be defined as follows. The vertices of Ga,b are V \{a, b, c} where {a, b, c} ∈ B. {x, y} is an edge if either {a, x, y} or {b, x, y} ∈ B. The Steiner triple system is said to be perfect if the cycle graph of every pair is a single (v − 3)-cycle. Perfect STS(v) are known only for v = 7, 9, 25 and 33. We ...

An S-colouring of a cubic graph G is an edge-colouring of G by points of a Steiner triple system S such that the colours of any three edges meeting at a vertex form a block of S. In this note we present an infinite family of point-intransitive Steiner triple systems S such that (1) every simple cubic graph is S-colourable and (2) no proper subsystem of S has the same property. Only one point-in...

We present mixed integer programming approaches for optimally solving a combinatorial optimization problem arising in network design with additional quality of service constraints. The rooted delayand delay-variation-constrained Steiner tree problem asks for a cost-minimal Steiner tree satisfying delay-constraints from source to terminals and a maximal variation-bound between particular termina...