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Regular number of line block graph of a graph

Author:

Muddebihal, M. H. and Abdul Gaffar

Subject Area:

Physical Sciences and Engineering

Abstract:

For any (p ,q) graph G, the vertices and blocks of a graph are called its members. The line block graph Lb(G) of a graph G as the graph whose set of vertices is the union of the set of edges and blocks of G and in which two vertices are adjacent if and only if the corresponding edges of G are adjacent or the corresponding members are incident. The regular number of Lb(G) is the minimum number of subsets into which the edge set of Lb(G) should be partitioned so that the subgraph induced by each subset is regular and is denoted by r_Lb(G). In this paper some results on r_Lb(G) were obtained and expressed in terms of elements of G.

Mathematics Subject Classification number: 05C69, 05C70

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