The Journal of the Indian Mathematical Society

Bohdan Zelinka

Abstract

Let M = || m_ij || be a (0, l)-matrix of order m x n. The term bigraph T(M) of M is the graph whose vertex set is the union of two disjoint sets V = {V₁,..., V_m) and W = {w₁,..., w_n} and in which the vertices v_i, w_j (1 ≤ i ≤ m, 1 ≤ j ≤ n) are adjacent if and only if m_ij = 1, while neither any two vertices of V, nor any two vertices of W are joined together by an edge.

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Bohdan Zelinka ¹

Affiliations
1 Department of Mathematics, Liberec, Czechoslovakia, CZ

Abstract

If G and H are graphs with the property that the identification of any vertex of G with an arbitrary vertex of H results in a unique graph (up to isomorphism), then we write G.H for the thus obtained graph. This definition is in [2], p. 23. The graph G.H is called the dot-composition of G and H, the graphs G and H are called dot-components of this graph.

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