The graphs considered in this article are undirected, finite and simple graphs. In this article we have proved that eccentricity energy of Bistar graph B n,n is 2 (3n + 1) 2 + 4 (n − 1). Also we have investigated eccentricity energy of some graphs related to Bistar graph.

Let G = be a graph, with and . An injective mapping is called an even-odd harmonious labeling of the graph G, if an induced edge mapping such that (i) is bijective mapping (ii) The graph acquired from this labeling is called even-odd harmonious graph. In this paper, we discovered some interesting results like H-graph, comb graph, bistar graph and graph for even-odd harmonious labeling.

The graphs considered in this article are undirected, finite and simple graphs. In this article we have proved that maximum eccentricity energy of bistar graph B n,n is 4 √ 9n + 1. Also we have investigated maximum eccentricity energy of some graphs related to bistar graph and globe graph.

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