مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Information Journal Paper

Title

TOTAL OUTER-CONNECTED DOMINATING SETS AND TOTAL OUTER-CONNECTED DOMINATION POLYNOMIALS OF COMPLETE BIPARTITE GRAPH K2, n

Pages

  208-216

Abstract

 Let G = (V, E) be a simple graph. A set D⊆V (G) is a total outer−connected dominating set of G if D is total dominating, and the induced sub-graph G[V (G) − D] is a connected graph. Let K2,n be the complete bipartite graph and D ̃tc (K2,n,i) denote the family of all total outer-connected dominating sets of K2,n with cardinality i. Let d ̃tc (K2,n,i)=|D ̃tc (K2,n,i)|. In this paper, we obtain recursive formula for d ̃tc (K2,n,i). Using this recursive formula, we construct the polynomial, D~tc (K2,n,x)=∑i=22+nd ̃tc (K2,n,i)xi  which we call total outer−connected domination polynomial of K2,n and obtain some  properties of this polynomial.

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