# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

Y.-Y. Tan, J.H. Koolen, Z.-J. Xia

Title:

A spectral characterization of the $s$-clique extension of the triangular graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2019-05-07, Revised: 2019-08-08, Accepted: 2019-08-09, https://doi.org/10.7151/dmgt.2273

Abstract:

A regular graph is co-edge regular if there exists a constant $\mu$ such that any two distinct and non-adjacent vertices have exactly $\mu$ common neighbors. In this paper, we show that for integers $s\ge 2$ and $n$ large enough, any co-edge-regular graph which is cospectral with the $s$-clique extension of the triangular graph $T(n)$ is exactly the $s$-clique extension of the triangular graph $T(n)$.

Keywords:

co-edge-regular graph, $s$-clique extension, triangular graph