Abstract
Objectives: To introduce connected -eccentric point set, connected -eccentric number, connected -eccentric dominating set, connected -eccentric domination number in a graph and related concepts. Methods: -distance in graphs are used to find the connected -eccentric number and connected -eccentric domination number in graphs. Findings: The new term connected -eccentric domination in graphs are used in varies field like to construct least number of cell phone tower in low cost and traffic signal also. Novelty: Using the idea -distance, eccentricity in a graphs, the connected -eccentric dominating set and its number in graphs are obtained. Some points, observation, bounds and theorem related to connected -eccentric domination set and its number in graphs are stated and proved. 2010 Mathematics Subject Classification: 05C12, 05C69 Keywords: D-eccentric node, D-eccentric node-set, D-eccentric dominating set, D-eccentric domination number, Connected D-eccentric dominating set, Connected D-eccentric domination number
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