Petersen-Torus as an interconnection network was extensively studied. This letter proposed two elementary algorithms for QoS routing in general Petersen-Torus networks, which can be modeled as graph ( , ) PT m n with K QoS parameters associated with each edge. Theoretic analysis for the proposed algorithms was conducted. And the time complexity of these two algorithms was summarized and compare...

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.

In this paper, we completely describe the spectrum of the generalized Petersen graph P (n, k), thus adding to the classes of graphs whose spectrum is completely known.

Let C(T ) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either Bn or Dn. Let CY (T ) be a natural quotient of C(T ), and if C(T ) is simply-laced (which means all the relations between the generators has order 2 or 3), CY (T ) is a generalized Coxeter group, too . Let At,n be a group which contains t Abelian groups generated by n elements. The...

We use graph homomorphisms and the chromatic properties of the Petersen graph to prove some inequalities on systems of sets. These inequalities are then used to find counterexamples to a conjecture of Albertson and Collins on the monotonicity of the chromatic difference sequence of a vertex-transitive graph.

A {em weak signed Roman dominating function} (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as afunction $f:V(G)rightarrow{-1,1,2}$ having the property that $sum_{xin N[v]}f(x)ge 1$ for each $vin V(G)$, where $N[v]$ is theclosed neighborhood of $v$. The weight of a WSRDF is the sum of its function values over all vertices.The weak signed Roman domination number of $G...

In this paper we establish a theorem on the maximum number of vertices of a generalized Petersen graph as a function of the diameter.

A signed bipartite graph is a bipartite graph in which each edge is assigned a positive or a negative sign. Let G(U, V ) be a signed bipartite graph with U = {u1, u2, · · · , up} and V = {v1, v2, · · · , vq} . Then signed degree of ui is sdeg(ui) = di = d + i − d − i , where 1 ≤ i ≤ p and d+i ( d − i ) is the number of positive(negative) edges incident with ui , and signed degree of vj is sdeg(...