The aim of this study is Decomposition of the changes in energy consumption with emphasizing the structural changes in Iran during 2001-2011 using Input-Output Structural Decomposition Analysis (I_O SDA). Structural changes in this study represent the changes in structure of intermediate input in sectors and also changes in structure of final demand categories. Structural changes in intermediate inputs decomposed into intermediate input substitution in sectors and changes in direct backward linkages. Structural changes in final demand represent the changes of the share of each sector in total final demand categories. The results showed that energy coefficients helped to reduce energy use and final demand changes and technological changes (structural changes in intermediate inputs) caused to increase of energy use. The final demand had the main contribution on increase of energy use (44186. 26 BGJ). Among the final demand components, increase in level of investment and household’ s consumption was the main drivers of energy use increment.

A difference labeling of a graph G is an injective function f: V (G) → N ∪ {0} together with the weight function f∗ on E(G) given by f∗(uv) = |f(u)-f(v)| for every edge uv in G. The collection of subgraphs induced by the edges of the same weight is a Decomposition of G and is called the common weight Decomposition of G induced by f. Let ϒf denote the collection of all the paths taken from each member of the common weight Decomposition induced by f. A difference labeling f of G is said to be a graphoidal difference labeling if ϒf is an acyclic graphoidal Decomposition of G. This paper initiates a study on this concepts.