Let G be a (p,q)-graph and k~O. A graph G is said to be k-edge­ graceful if the edges can be labeled by k,k+I, ... ,k+q-I so that the vertex sums are distinct, modulo p. We denote the set of all k such that G is k-edge graceful by egS(G). The set is called the edge-graceful spectrum ofG. In this paper, we are concerned with the problem of exhibiting sets of natural numbers which are the edge-gr...

Further, even though it is intellectually accepted that we have methodological means to combat these factors and provide benefits during the evolutionary process, development managers still choose short term goals over these long term benefits. Given a choice between getting a system out as early as possible and doing a proper design that will evolve gracefully, the first is invariably chosen a...

a graph g is said to have a totally magic cordial labeling with constant c if there exists a mapping f : v (g) ∪ e(g) → {0, 1} such that f(a) + f(b) + f(ab) ≡ c (mod 2) for all ab ∈ e(g) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. in this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...

We present the first polynomial time construction procedure for generating graceful double-wheel graphs. A graph is graceful if its vertices can be labeled with distinct integer values from {0, ..., e}, where e is the number of edges, such that each edge has a unique value corresponding to the absolute difference of its endpoints. Graceful graphs have a range of practical application domains, i...