All hypoenergetic graphs with maximum degree at most 3 |
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Authors: | Xueliang Li Hongping Ma |
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Institution: | aCenter for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin 300071, PR China |
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Abstract: | The energy E(G) of a graph G is defined as the sum of the absolute values of its eigenvalues. A connected graph G of order n is said to be hypoenergetic if E(G)<n. All connected hypoenergetic graphs with maximum degree Δ 3 have been characterized. In addition to the four (earlier known) hypoenergetic trees, we now show that complete bipartite graph K2,3 is the only hypoenergetic cycle-containing hypoenergetic graph. By this, the validity of a conjecture by Majstorović et al. has been confirmed. |
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Keywords: | Energy of a graph Hypoenergetic Quadrangle-containing (-free) Cyclomatic number |
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