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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 $sge 2$ 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 $T(n)$.
In this paper we show that for integers $sgeq2$, $tgeq1$, any co-edge-regular graph which is cospectral with the $s$-clique extension of the $ttimes t$-grid is the $s$-clique extension of the $ttimes t$-grid, if $t$ is large enough. Gavrilyuk and Koo
Let $P_n$ and $C_n$ denote the path and cycle on $n$ vertices respectively. The dumbbell graph, denoted by $D_{p,k,q}$, is the graph obtained from two cycles $C_p$, $C_q$ and a path $P_{k+2}$ by identifying each pendant vertex of $P_{k+2}$ with a ver
Let $G$ be a graph whose edges are coloured with $k$ colours, and $mathcal H=(H_1,dots , H_k)$ be a $k$-tuple of graphs. A monochromatic $mathcal H$-decomposition of $G$ is a partition of the edge set of $G$ such that each part is either a single edg
Let $q_{min}(G)$ stand for the smallest eigenvalue of the signless Laplacian of a graph $G$ of order $n.$ This paper gives some results on the following extremal problem: How large can $q_minleft( Gright) $ be if $G$ is a graph of order $n,$ with n
Given a graph $G$, the strong clique number of $G$, denoted $omega_S(G)$, is the maximum size of a set $S$ of edges such that every pair of edges in $S$ has distance at most $2$ in the line graph of $G$. As a relaxation of the renowned ErdH{o}s--Nev{