Characterizations and Edge Partitions of the Boolean Graphs BG2(G), BG3(G) and their Complements

T.N.Janakiraman, M.Bhanumathi, S.Muthammai


Volume :5 , Issue :1 ,Page :1-23



Abstract :Let G be a simple (p, q) graph with vertex set V(G) and edge set E(G). B G, INC,  L(G) (G) is a graph with vertex set V(G)  E(G) and two vertices are adjacent if and only if they correspond to two adjacent vertices of G, to a vertex and an edge incident to it in G or two non-adjacent edges of G. For simplicity, denote this graph by BG 2 (G), Boolean graph of G-second kind. Similarly, B  K p , INC,  L(G)(G) is a graph with the same vertex set and two vertices are adjacent if and only if they correspond to a vertex and an edge incident to it in G or two non-adj acent edges of G. For simplicity, denote this graph by BG 3 (G), Boolean graph of G-third kind. In this paper, characterizations of BG 2 (G), BG 3 (G) and partitions of edges of BG 2 (G), BG 3 (G) and their complements are studied.



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