Nowhere‐zero flows in tensor product of graphs

Abstract

Abstract:In this paper, we characterize graphs whose tensor product admit nowhere-zero 3-flow. The main result is: For two graphs G 1 and G 2 with δ G 1 ≥ 2 and G 2 not belonging to a well-characterized class of graphs, the tensor product of G 1 and G 2 admits a nowhere-zero 3-flow.

NZ‐flows in strong products of graphs

“…In [10] it is shown that the direct product of nontrivial graphs admits an NZ 3-flow if one factor does not have any leafs and the other is not a member of a certain family of trees.…”

Nowhere-zero 3-flows in semistrong product of graphs

“…was investigated by Zhang et al [17] and Imrich et al [4], respectively. More results on nowhere-zero 3-flows and group connectivity of products of graphs can be found in [9,15,16] and others.…”

Flows on the join of two graphs

“…The 3-flow conjecture has received somewhat less attention. Perhaps the lack of progress in this area has motivated several authors to examine flow numbers of graphs resulting from various graph operations, most notably graph products [5], [6], [10], [12], [15], [20]. Very recently Thomassen proved the 3-flow conjecture for 8-edge-connected graphs [17].…”