{'fraction_non_alphanumeric': 0.027227722772277228, 'fraction_numerical': 0.0, 'mean_word_length': 3.932926829268293, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
CONNECTED DOMINATION POLYNOMIAL OF A GRAPH

L et G = (V, E) be a simple connected graph of order n. A connected dominating set of G is a set S of vertices of G such that every vertex in V − S is adjacent to some vertex in S and the induced subgraph a S n is connected. The connected domination number i c (G) is the minimum cardinality of a connected dominating set of G. In this paper we introduce the connected domination polynomial of G. The connected domination polynomial of a connected graph G of order n is the polynomial D c (G, x) =  where d c (G, i) is the number of connected dominating set of G of size i and i c (G) is the connected domination number of G. We obtain some basic properties of the connected domination polynomial and compute this polynomial and its roots for some standard graphs.