The well-known Euler characteristic is an invariant of graphs defined by means of the vertex, edge and face numbers of a graph, to determine the genus of the underlying surface of the graph. By means of it, it is possible to determine the vertex, edge and face numbers of all possible graphs which can be drawn in a given orientable/nonorientable surface. In this paper, by means of a given degree sequence, a new number denoted by ( ) which is related to Euler characteristic and has several

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... tions in Graph Theory is defined. This formula gives direct information compared with the Euler characteristic on the realizability, number of realizations, connectedness, being acyclic or cyclic, number of components, chords, loops, pendant edges, faces, bridges etc.