Star graphs are Cayley graphs of symmetric groups of permutations, with transpositions as the generating sets. A star graph is a preferred interconnection network topology to a hypercube for its ability to connect a greater number of nodes with lower degree. However, an attractive property of the hypercube is that it has a Hamiltonian decomposition, i.e. its edges can be partitioned into disjoi...

In this paper, we present efficient layouts for complete graphs and star graphs. We show that an N-node complete graph can be optimally laid out using LN2/4] tracks for a colinear layout, and can be laid out in N4/16 + o(N4) area for a 2D layout. We also show that an N-node star graph can be laid out in N2/16 + o(N2) area, which is smaller than any possible layout of a similar-size hypercube. T...

In this paper we compute the number of spanning trees of a specific family of graphs using techniques from linear algebra and matrix theory. More specifically, we consider the graphs that result from a complete graph K, after removing a set of edges that spans a multi-star graph K,,, (al, ~2, . , a,). We derive closed formulas for the number of spanning trees in the cases of double-star (m = 2)...

The concept of star chromatic number of a graph, introduced by Vince (1988) is a natural generalization of the chromatic number of a graph. This concept was studied from a pure combinatorial point of view by Bondy and Hell (1990). In this paper we introduce strong and weak star chromatic numbers of uniform hypergraphs and study their basic properties. In particular, we focus on partial Steiner ...

Let G = (V,E) be a simple connected graph. The eccentric-distance sum of G is defined as ξ(G) = ∑ {u,v}⊆V (G) [e(u) + e(v)]d(u, v), where e(u) is the eccentricity of the vertex u in G and d(u, v) is the distance between u and v. In this paper, we establish formulae to calculate the eccentric-distance sum for some graphs, namely wheel, star, broom, lollipop, double star, friendship, multi-star g...