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Graphs with the Same Detour Matrix

Milan Randić ; Department of Mathematics and Computer Science, Drake University, Des Moines, LA 50311
Luz M. DeAlba ; Department of Mathematics and Computer Science, Drake University, Des Moines, LA 50311
Frank E. Harris ; Department of Chemistry and Department of Physics, University of Utah, Salt Lake City, UT 84112

Sažetak

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 sum of all entries above the main diagonal gives the detour index dd. Distinct graphs that have the same detour index have been reported in the literature. We examined such graphs and others that we have found and report on some of their regularities. We noticed that many graphs have not only the same detour index but also the same detour matrix. We considered in particular graphs for which the elements of the detour matrix are maximal. Such graphs are called saturated graphs. The detour matrix of a saturated graph is the same as that of the complete graph having the same number or vertices.

Ključne riječi

Hrčak ID:

132324

URI

https://hrcak.srce.hr/132324

Datum izdavanja:

2.3.1998.

Posjeta: 1.046 *