Oriented diameter of star graphs

Oriented diameter of graphs with diameter 3

In 1978, Chvátal and Thomassen proved that every 2-edge-connected graph with diameter 2 has an orientation with diameter at most 6. They also gave general bounds on the smallest value f(d) such that every 2-edge-connected graph G with diameter d has an orientation with diameter at most f(d). For d = 3, their general bounds reduce to 8 ≤ f(3) ≤ 24. We improve these bounds to 9 ≤ f(3) ≤ 11.

Oriented graphs of diameter 2

Let f(n) be the minimum number of arcs among oriented graphs of order n and diameter 2. Here it is shown for n > 8 that (1−o(1))nlog2n ≤ f(n) ≤ nlog2n− (3/2)n. ∗1991 Mathematics Subject Classification. Primary 05C20, 05C35, 05C15; Secondary 05D99

On Diameter of Line Graphs

The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.

Leader election in oriented star graphs

Leader election in a network plays an important role in the area of distributed algorithm design. Structural properties of the network as well as presence of direction on the edges of the network greatly affects the complexity of the leader election problem which is primarily measure by the message complexity of the protocol. Our purpose in the present paper is to adapt the existing distributed...

The omplexity of approximating the oriented diameter of hordal graphs