(DOWNLOAD) "Singed Total Domatic Number of a Graph (Report)" by H.B. Shirkol, Shailaja S. Narayankar, Kishori P. Walikar ~ eBook PDF Kindle ePub Free
eBook details
- Title: Singed Total Domatic Number of a Graph (Report)
- Author : H.B. Shirkol, Shailaja S. Narayankar, Kishori P. Walikar
- Release Date : January 01, 2010
- Genre: Mathematics,Books,Science & Nature,
- Pages : * pages
- Size : 63 KB
Description
[section]1. Terminology and Introduction Various numerical invariants of graphs concerning domination were introduced by means of dominating functions and their variants [1] and [4]. We considered finite, undirected, simple graphs G = (V, E) with vertex set V(G) and edge set E(G). The order of G is given by n = [absolute value of V(G)]. If v [member of] V(G), then the open neighborhood of v is N(v) = {u [member of] V(G)\uv [member of] E(G)} and the closed neighborhood of v is N[v] = {v} [union] N(v). The number [d.sub.G](v) = d(v) = [absolute value of N(v)] is the degree of the vertex v [member of] V(G), and [delta](G) is the minimum degree of G. The complete graph and the cycle of order n are denoted by [K.sub.n] and [C.sub.n] respectively. A fan and a wheel is a graph obtained from a path and a cycle by adding a new vertex and edges joining it to all the vertices of the path and cycle respectively. The generalized Petersen graph P(n, k) is defined to be a graph on 2n vertices with V(P(n, k)) = {[v.sub.i][u.sub.i] : 1 [less than or equal to] i [less than or equal to] n} and E(P(n, k)) = {[v.sub.i][v.sub.i+1], [v.sub.i][u.sub.i], [u.sub.i][u.sub.i+k] : 1 [less than or equal to] i [less than or equal to] n, subscripts modulo n}. If A [subset or equal to] V(G) and f is a mapping from V(G) in to some set of numbers, then f(A) = [[summation].sub.x[member of][A]f(x).
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