University of IsfahanTransactions on Combinatorics2251-86572320130901Energy of binary labeled graphs5367329210.22108/toc.2013.3292ENPradeep G.BhatManipal Institute of Technology
Manipal University0000 0003 2179 6207SabithaD'SouzaManipal Institute of Technology,
Manipal UniversityJournal Article20130712Let $G$ 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 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.https://toc.ui.ac.ir/article_3292_782073aa78bf670706945d083a62986b.pdf