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Vertex coloring of a graph $G$ with $n$-colors can be equivalently thought tobe a graph homomorphism (edge preserving vertex mapping) of $G$ to the completegraph $K_n$ of order $n$. So, in that sense, the chromatic number $\chi(G)$ of$G$ will be the order of the smallest complete graph to which $G$ admits ahomomorphism to. As every graph, which is not a complete graph, admits ahomomorphism to a smaller complete graph, we can redefine the chromatic number$\chi(G)$ of $G$ to be the order of the smallest graph to which $G$ admits ahomomorphism to. Of course, such a smallest graph must be a complete graph asthey are the only graphs with chromatic number equal to their order.  The concept of vertex coloring can be generalize for other types of graphs.Naturally, the chromatic number is defined to be the order of the smallestgraph (of the same type) to which a graph admits homomorphism to. The analogousnotion of clique turns out to be the graphs with order equal to their (sodefined) "chromatic number". These "cliques" turns out to be much morecomplicated than their undirected counterpart and are interesting objects ofstudy. In this article, we mainly study different aspects of "cliques" forsigned (graphs with positive or negative signs assigned to each edge) andswitchable signed graphs (equivalence class of signed graph with respect toswitching signs of edges incident to the same vertex).

Analogous to cliques for (m,n)-colored mixed graphs