In this paper we find the number of different signatures P (3, 1), (5, 1) and (7, up to switching isomorphism, where ( n , k ) denotes generalised Petersen graph, 2 < . We also count non-isomorphic on (2 + 1, size two for all ≥ 1 conjecture that any signature switching, is at most

The crossing number of a graph G in surface Σ, denoted by crΣ(G), is the minimum pairwise intersections edges drawing Σ. Let k be an integer satisfying k≥3, generalized Petersen P(3k,k) with vertex set V(P(3k,k))={ui,vi∣i=1,2,…,3k} and edge E(P(3k,k))={uiui+1,uivi,vivk+i∣i=1,2,…,3k}, subscripts are read modulo 3k. In this paper we investigate projective plane. We determine exact value crN1(P(3k...

An antimagic labeling of a finite simple undirected graph with q edges is a bijection from the set of edges to the set of integers {1, 2, · · · , q} such that the vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of labels of all edges incident to such vertex. A graph is called antimagic if it admits an antimagic labeling. It was conjectured by N. Hartsfield and G. ...

In 1995, Brouwer proved that the toughness of a connected k-regular graph G is at least k/λ − 2, where λ is the maximum absolute value of the non-trivial eigenvalues of G. Brouwer conjectured that one can improve this lower bound to k/λ − 1 and that many graphs (especially graphs attaining equality in the Hoffman ratio bound for the independence number) have toughness equal to k/λ. In this pape...

Abstract A multilevel distance labeling of the graph G is a function f = (V (G),E(G)) on V (G) of G into N ∪ {0} so that |f(u) − f(v)| ≥ diam(G) + 1− d(u, v) for all u, v ∈ V (G). The smallest span taken over all multilevel distance labeling of G is radio number rn(G) of G. In this paper, we completely determine the radio number rn(G) of G where G is the graph obtained from generalized Petersen...

The purpose of the independent set interdiction problem in the weighted graph G is to determine a set of vertices R∗ such that the weight of the maximum independent set in G−R∗ is minimized. We define an approximate solution for this problem. Then, an upper bound for the relative error of this problem is obtained. We show that the limit of the relative error of the independent set interdiction ...

R. Bruce Richter Department of Mathematics and Statistics, Carleton University, Ottawa, Canada K1S 5B6 and Gelasio Salazar1 School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30319 and IICO{UASLP, San Luis Potosi, Mexico 78000 21 April 1999 Abstract. It is proved that the crossing number of the Generalized Petersen Graph P (3k+ h; 3) is k + h if h 2 f0; 2g and k + 3 if h = 1, f...