“School of Mathematics”
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| Paper IPM / M / 9498 |
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| Abstract: | |
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The energy of a graph E(G), is the sum of the singular values of its adjacency matrix. We define incidence energy of the graph G, denoted by IE(G), as the sum of the singular values of its incidence matrix. We are interested to find the relation between the energy and the incidence energy of graphs. For any graph G we obtain a bipartite graph ∧G such that
IE(G) = [(E(∧G))/2] . Moreover we ?nd some similar upper and lower bounds of energy
for incidence energy. Finally we show that for any proper subgraph H of the graph G, IE(G) > IE(H).
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