On Detour Spectra of Some Graphs

The Detour matrix (DD) of a graph has for its ( i , j) entry the length of the longest path between vertices i and j. The DD-eigenvalues of a connected graph G are the eigenvalues for its detour matrix, and they form the DD-spectrum of G. The DD-energy EDD of the graph G is the sum of the absolute values of its DDeigenvalues. Two connected graphs are said to be DD- equienergetic if they have equal DD-energies. In this paper, the DD- spectra of a variety of graphs and their DD-energies are calculated.

Authors:

• S.K.Ayyaswamy
• S.Balachandran

Keywords:

• Detour eigenvalue (of a graph)
• detour spectrum(of a graph)
• detour energy(of a graph)
• detour - equienergetic graphs.

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