Minimum covering energy of binary labeled graph

Let $G$ be a graph with vertex set $V(G)$ and edge set $X(G)$ and consider the set $A={0,1}$. A mapping $l:V(G)longrightarrow A$ is called a binary vertex labeling of $G$ and $l(v)$ is called the label of the vertex $v$ under $l$. In this paper we introduce a new kind of graph energy for the binary labeled graph, the minimum covering label energy $E_{cl}(G)$. Depending on the underlying graph $G$ and its binary labeling, the upper and lower bounds for $E_{cl}(G)$ are established. The minimum covering label energies of complete and star graphs are computed. The characteristic polynomial of complete bipartite graph is also obtained.