Read More
Date: 26-4-2022
1400
Date: 15-5-2022
1397
Date: 9-3-2022
1618
|
The detour polynomial of a graph is the characteristic polynomial of the detour matrix of .
Precomputed detour polynomials for many named graphs are available in the Wolfram Language as GraphData[graph, "DetourPolynomial"].
Since a Hamilton-connected graph with vertex count has all off-diagonal matrix elements equal to , the detour polynomial of such a graph is given by .
The following table summarizes detour polynomials for some common classes of graphs. Here, is a Chebyshev polynomial of the first kind and is a Chebyshev polynomial of the second kind.
graph | detour polynomial |
Andrásfai graph | |
antiprism graph | |
barbell graph | |
book graph | |
cocktail party graph | |
complete bipartite graph | |
complete graph | |
complete tripartite graph | |
crossed prism graph | |
crown graph for | |
gear graph | |
halved cube graph | |
helm graph | |
hypercube graph | |
Keller graph | |
king graph | |
Möbius ladder | |
Mycielski graph | |
odd graph | |
path graph | |
prism graph | |
Sierpiński tetrahedron graph | |
star graph | |
wheel graph |
The following table summarizes the recurrence relations for detour polynomials for some simple classes of graphs.
graph | order | recurrence |
path graph | 5 |
Nikolić, S.; Trinajstić, N.; and Mihalić, A. "The Detour Matrix and the Detour Index." Ch. 6 in Topological Indices and Related Descriptors in QSAR and QSPR (Ed. J. Devillers A. T. and Balaban). Amsterdam, Netherlands: Gordon and Breach, pp. 279-306, 2000.
|
|
طقطقة الرقبة.. عواقب خطيرة جدا لا يمكن تخيلها
|
|
|
|
|
"ستارلاينر" تترك رائدين عالقين في الفضاء وتعود للأرض
|
|
|
|
|
بالصور: إقبال كبير على تلقي الخدمات الطبية في مستشفى سفير الإمام الحسين (ع)
|
|
|