A connected and nonempty graph A is defined as generalized t-edge distance-balanced, while for each edge f={ \alpha}\{ beta} the number of edges nearer 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 such graphs. Moreover, we investigate edge-szeged index of the generalized t-edge distance-balanced graphs. Also, it is discussed about their cartesian and lexicographic products.
Categories: math.CO