Satyanarayana , Bhavanari and Srinivasulu, Devanaboina and Kuncham, Syam Prasad and Setty, Eswaraiah S (2012) Some Results on Degree of Vertices in Semitotal-Block Graph and Total-Block Graph. International Journal of Computer Applications, 50 (9). pp. 19-22. ISSN 0975 – 8887

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Abstract

We considersemitotal-block graph, total-block graph of a graph G (respectively, denoted as Tb(G), TB(G)). We prove that the number of edges in a semitotal-block graph of a given graph G is equal to |E(G)| + |V(B1)| + |V(B2)| + … + |V(Bm)|, where B1, B2, …, Bm are the blocks of G. Further, we obtain that TB(G) is the ring sum of Tb(G) and the block graph B(G). We introduce the concept “vertex-block graph (denoted by Bv(G) of G)”, andwe prove thatTb(G) is the ring sum of G and Bv(G). We also present some related fundamental results along with illustrations.

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