Connected Total Dominating Sets and Connected Total Domination Polynomials of Square of Paths

Abstract

Let G be a simple connected graph of order n. Let D ct (G, i) be the family of connected total dominating sets in G with cardinality i. The polynomial D ct (G, x) = n i (G) ct   2 n P of cardinality i and some properties of this polynomial have been studied.

Vertex Connected Domination Polynomial of some Coalescence of Complete and Wheel Graphs

“…is the vertex connected domination number of We have: If (1,3), (1,4), (1,5)}|=4, If (1,2,4), (1,2,5), (1,3,4), (1,3,5), ( 1,4,5)}|=6, If (1,2,3,4), (1,2,3,5), (1,2,4,5), (1,3,4,5)}|=4, If…”

“…2. ( : , 4) (1,2,4,5), (1,3,4,5), (1,4,5,6), (1,4,5,7), (1,4,5,8), (2,3,4,5), (2,4,5,6), (2,4,5,7), (2,4,5,8), (3,4,5,6), (3,4,5,7), (3,4,5,8)…”

“…And the connected dominating set and connected domination polynomial was introduced in [9]. For more information and motivation of domination polynomial and connected domination polynomial refer to [1,2,3,4,7,10,11,13,14,15].…”