# Journal of the Ramanujan Mathematical Society

Volume 36, Issue 4, December 2021 pp. 325–330.

Connectivity of the tensor product of a graph and a cycle

**Authors**:
A. V. Sonawane and Y. M. Borse

**Author institution:**Government of Maharashtra's Ismail Yusuf College of Arts,
Science and Commerce, Mumbai 400 060, India

**Summary: **
In this paper, we determine the connectivity of the tensor product
G × C of any connected graph G and a cycle C. We obtain
the exact value of the connectivity of G × C when G is a
bipartite graph or C is an even cycle, and provide sharp bounds
for the connectivity when G is a non-bipartite graph and C is
an odd cycle. As a consequence, we prove that the connectivity of
the tensor product of k odd cycles is 2{k}.

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