L(2,1)-Circular Labelings of Certain Generalized Petersen Graphs P(n, 2)

摘要

For positive integers p and q with p >= q, a k-(p, q)-circular labeling of a graph G is a function f: V(G) -> {0, 1, 2,..., k - 1} such that vertical bar f (u) - f(v)vertical bar k >= p if u and v are adjacent; and vertical bar f(u) - f(v)vertical bar(k) >= q if u and v are at distance two, where vertical bar X vertical bar(k) = min{vertical bar X vertical bar, k vertical bar X vertical bar}. The minimum integer k such that there exists an k-(p, q)-circular labeling of G is called the sigma(p,q)-number of G and is denoted by sigma(p,q)(G). This paper determines the exact value of sigma(2,1)-number of generalized Peterson graphs P(n, 2).