Energy of binary labeled graphs

‎‎‎Let G be a graph with vertex set V(G) and edge set X(G) and consider the set A=\{۰,۱\}‎. ‎A mapping l:V(G)\longrightarrow A is called 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 labeled graph energy E_{l}(G)‎. ‎It depends on the underlying graph G and on its binary labeling‎, ‎upper and lower bounds for E_{l}(G) are established‎. ‎The labeled energies of a number of well known and much studied families of graphs are computed‎.

Keywords:

‎Label Matrix‎ , ‎Label Eigenvalues‎ , ‎Label Energy