Abstract
In this paper it is observed that blocks behave like an edge of a graph with multiple vertices. This intutive notion of analogy between blocks and edges of a graph motivated to define block paths in a graph. It is observed that every graph is a block tree (B-Tree). Varieties of block-degrees and expressions for sum of block degrees are obtained. New graphs, semitotal-block-cutvertex graph, total-block-cutvertex graph and semitotal block-vertex-edge graph arising from the given graph are defined and expressions for the number of edges in the new graphs are derived. Several bounds for number of blocks and cutvertices in a graph are obtained. A new class of graphs called block regular graphs are introduced and their properties are studied.
| Original language | English |
|---|---|
| Pages (from-to) | 20-31 |
| Number of pages | 12 |
| Journal | Global and Stochastic Analysis |
| Volume | 12 |
| Issue number | 3 |
| Publication status | Published - 05-2025 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Discrete Mathematics and Combinatorics