In this paper we refine the notion of tree-decomposition by introducing acyclic (R,D)-clustering, where clusters are subsets of vertices of a graph and R and D are the maximum radius and the maximum diameter of these subsets. We design a routing scheme for graphs admitting induced acyclic (R,D)-clustering where the induced radius and the induced diameter of each cluster are at most 2. We show t...

Two new species of the genus Eotmethis Bey-Bienko, 1948, namely Eotmethis xiai sp. nov., and Eotmethis platyverticus sp. nov. from the Ningxia Hui Autonomous Region and Gansu province are described in this paper. The new species Eotmethis xiai sp. nov. is allied to E. recipennis Xi & Zheng, 1986, but differs from latter by the vertical diameter of eye about 1.2 times as long as horizontal diame...

Let G be a unit-distance graph in R2. For each unit-distance representation of G in R2, there is a smallest circumscribing circle. The infimum of the diameters of these circles, taken over all unit-distance representations of G, is called the span of G. On the other hand, the supremum of the diameters of all such circles is called the extent of G. We show that the ratio of the extent to the dia...

For any graph G, the Equi-eccentric point set graph Gee is defined on the same set of vertices by joining two vertices in Gee if and only if they correspond to two vertices of G with equal eccentricities. The Glue graph Gg is defined on the same set of vertices by joining two vertices in Gg if and only if they correspond to two adjacent vertices of G or two adjacent vertices of Gee. In this pap...

Let r , k be positive integers, s(< r), a nonnegative integer, and n=2r−s+k. The set of r-subsets of [n]={1, 2, . . . , n} is denoted by [n]r . The generalized Kneser graphK(n, r, s) is the graph whose vertex-set is [n]r where two r-subsets A and B are joined by an edge if |A ∩ B| s. This note determines the diameter of generalized Kneser graphs. More precisely, the diameter of K(n, r, s) is eq...