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A connected and nonempty graph A is defined as generalized t-edgedistance-balanced, while for each edge f={\alpha}\{beta} the number of edgesnearer to {\alpha} than \{beta} are equal to t-times of edges nearer to \{beta}than to {\alpha}, for t \in N, or vice versa. We determine some classes of suchgraphs. Moreover, we investigate edge-szeged index of the generalized t-edgedistance-balanced graphs. Also, it is discussed about their cartesian andlexicographic products.

Generalized T-Edge Distance-Balanced Graphs