• Kyungpook Mathematical Journal
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• 제48권2호
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• pp.303-315
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• 2008

In [8] M. Y. Alzoubi and M. M. Jaradat studied the basis number of the composition of paths and cycles with Ladders, Circular ladders and M$\"{o}$bius ladders. Namely, they proved that the basis number of these graphs is 4 except possibly for some cases in each of them. Since the lexicographic product is noncommutative, in this paper we investigate the basis number of the lexicographic product of the different kinds of ladders with paths and cycles. In fact, we prove that the basis number of almost all of these graphs is 4.

• 대한수학회보
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• 제59권3호
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• pp.685-695
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• 2022

The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b(G). A known lower bound on b(G) states that b(G) ≥ max{p(G), q(G)}, where p(G) and q(G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b(G) = max{p(G), q(G)} + 1, G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness and almost eigensharpness of lexicographic products of some graphs.

• 충청수학회지
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• 제14권1호
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• pp.7-14
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• 2001

Let G be a connected graph. A pebbling move on a graph G is taking two pebbles off one vertex and placing one of them on an adjacent vertex. The pebbling number of a connected graph G, f(G), is the least n such that any distribution of n pebbles on the vertices of G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. In this paper, the pebbling numbers of the lexicographic products of some graphs are computed.