Generalized T-Edge Distance-Balanced Graphs (2312.14863v1)

Abstract: 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.