Xirong Xu

Radio number of ladder graphs

Let G be a connected graph with diameter diam(G). The radio number for G, denoted by rn(G), is the smallest integer k such that there exists a function f: V(G)→{0, 1, 2, …, k} with the following satisfied for all vertices u and v:|f(u)−f(v)|≥diam (G)−d G (u, v)+1, where d G (u, v) is the distance between u and v in G. In this paper, we determine the radio number of ladder graphs.

On the distance paired domination of generalized Petersen graphs P(n,1) and P(n,2)

Let G=(V,E) be a graph without an isolated vertex. A set D⊆V(G) is a k-distance paired dominating set of G if D is a k-distance dominating set of G and the induced subgraph 〈D〉 has a perfect matching. The minimum cardinality of a k-distance paired dominating set for graph G is the k-distance paired domination number, denoted by γpk(G). In this paper, we determine the exact k-distance paired domination number of generalized Petersen graphs P(n,1) and P(n,2) for all k≥1.

The crossing number of the generalized Petersen graph P10, 3 is six

The crossing number of a graph is the least number of crossings of edges among all drawings of the graph in the plane. In this article, we prove that the crossing number of the generalized Petersen graph P(10, 3) is equal to 6.