| Autor: |
Alizadeh, Yaser, Klavžar, Sandi, Langari, Javaher |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
For a positive integer $k\ge 1$, a graph $G$ is $k$-stepwise irregular ($k$-SI graph) if the degrees of every pair of adjacent vertices differ by exactly $k$. Such graphs are necessarily bipartite. Using graph products it is demonstrated that for any $k\ge 1$ and any $d \ge 2$ there exists a $k$-SI graph of diameter $d$. A sharp upper bound for the maximum degree of a $k$-SI graph of a given order is proved. The size of $k$-SI graphs is bounded in general and in the special case when $\gcd(\Delta(G), k) = 1$. Along the way the degree complexity of a graph is introduced and used. |
| Databáze: |
arXiv |
| Externí odkaz: |
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