## Taiwanese Journal of Mathematics

### Graphs with Isomorphic Neighbor-subgraphs

#### Abstract

A graph $G$ is said to be $H$-regular if for each vertex $v \in V(G)$, the graph induced by $N_G(v)$ is isomorphic to $H$. A graph $H$ is a feasible neighbor-subgraph if there exists an H-regular graph, otherwise $H$ is a forbidden neighbor-subgraph. In this paper, we obtain some classes of graphs $H$ which are forbidden and then we focus on searching $H$-regular graphs especially those graphs of smaller order.

#### Article information

Source
Taiwanese J. Math., Volume 15, Number 3 (2011), 1171-1182.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406293

Digital Object Identifier
doi:10.11650/twjm/1500406293

Mathematical Reviews number (MathSciNet)
MR2829905

Zentralblatt MATH identifier
1235.05112

Keywords
neighbor isomorphic subgraphs

#### Citation

Chan, Chi-Feng; Fu, Hung-Lin; Li, Chao-Fang. Graphs with Isomorphic Neighbor-subgraphs. Taiwanese J. Math. 15 (2011), no. 3, 1171--1182. doi:10.11650/twjm/1500406293. https://projecteuclid.org/euclid.twjm/1500406293

#### References

• C. Godsil and G. Royle, Algebraic Graph Theory, Springer, 2001.
• R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, England: Oxford University Press, 1998.
• D. B. West, Introduction to Graph Theory, Prentice Hall, 1996.