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- Title
On Some Properties of Edge Quasi-Distance-Balanced Graphs.
- Authors
Aliannejadi, Z.; Gilani, A.; Alaeiyan, M.; Asadpour, J.
- Abstract
For an edge e = uv in a graph G, MGu (e) is introduced as the set all edges of G that are at shorter distance to u than to v. We say that G is an edge quasi-distance-balanced graph whenever for every arbitrary edge e = uv, there exists a constant λ > 1 such that mGu(e) = λ+1 mGv (e). We investigate that edge quasi-distance-balanced garphs are complete bipartite graphs Km, n with m = n. The aim of this paper is to investigate the notion of cycles in edge quasi-distance-balanced graphs, and expand some techniques generalizing new outcome that every edge quasi-distance-balanced graph is complete bipartite graph. As well as, it is demontrated that connected quasi-distance-balanced graph admitting a bridge is not edge quasi-distance-balanced graph.
- Subjects
GEOMETRIC vertices; GRAPH theory; RATIONAL numbers; BIPARTITE graphs; PARTITIONS (Mathematics)
- Publication
Journal of Mathematical Extension, 2022, Vol 16, Issue 8, p1
- ISSN
1735-8299
- Publication type
Article