Tensor product of graphs

The tensor product of graphs is a graph formed by taking the Cartesian product of the vertex sets of two graphs G and H, and adding edges between vertices (g,h) and (g',h') if and only if g is adjacent to g' in G and h is adjacent to h' in H.From: Graph Theory and Interconnection Networks [2019], Tensor and Cartesian products for nanotori, nanotubes and zig–zag polyhex nanotubes and their applications to ¹³C NMR spectroscopy [2021]

Wiener Index of Tensor Product of Cycle Graph and Some Other Graphs

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Published in N. P. Shrimali, Nita H. Shah, Recent Advancements in Graph Theory, 2020

H. S. Mehta, J. George

The tensor product of graphs is a very well-known graph product and has been studied in detail. Also the Wiener index of a connected graph G is defined as, W(G)=∑{x,x′}⊂V(G)d(x,x′). In this chapter, we obtain W(C2m+1 ⊗ H) for any connected, bipartite graph H with diameter at most 4. Also, we obtain W(C2m+1 ⊗ H) for some non-bipartite graphs H as the wheel graph Wn, Helm graph Hn etc.

Tensor and Cartesian products for nanotori, nanotubes and zig–zag polyhex nanotubes and their applications to ¹³C NMR spectroscopy

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Journal Information

Published in Molecular Physics, 2021

Medha Itagi Huilgol, V. Sriram, Krishnan Balasubramanian

The tensor product of graphs G and H is a graph such that the vertex set of is the Cartesian product and vertices and are adjacent in if and only if g is adjacent to and h is adjacent to .

Tensor product of graphs

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Wiener Index of Tensor Product of Cycle Graph and Some Other Graphs

Tensor and Cartesian products for nanotori, nanotubes and zig–zag polyhex nanotubes and their applications to 13C NMR spectroscopy

Tensor and Cartesian products for nanotori, nanotubes and zig–zag polyhex nanotubes and their applications to ¹³C NMR spectroscopy