arXiv subjects
Publications and source records attributed to Mehdi Alaeiyan.
A nonempty graph G is called generalized 3-distance-balanced, (3-GDB) whenever for every edge ab, |Wab|=3|Wba| or conversely. As well as a graph G is called generalized 3-nicely distance-balanced (3-GNDB) whenever for every edge ab of G, there exists a positive integer g, such that: |Wba|=gG. In this paper, we classify 3-GNDB graphs with, gG \in{1,2}.
A connected and nonempty graph A is defined as generalized t-edge distance-balanced, while for each edge f=α\{beta} the number of edges nearer to α than \{beta} are equal to t-times of edges nearer to \{beta} than to α, 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.