1-Quasitotal graphs vs. degree of vertices with respect to a vertex set

In [Satyanarayana Bhavanari, 2014] the authors Satyanarayana, Srinivasulu and Syam Prasad studied 1–quasitotal graphs and in [Rajeshkanna et al., 2013] the authors Rajesh kanna, Dharmendr, Sridhara and Pradeep kumar studied the concepts ‘degree of a vertex with respect to a given vertex set’. Some examples related to 1–quasitotal graphs and the degree of vertices of these graphs with respect to a particular given vertex set were presented. Finally we obtained a theorem whose statement is as follows: (i) If A=V(G) and A⊆V(Q_1 (G)), then d_A (v) = d_(Q_1 (G) ) (v) for all v∈ V(G) and d_A (v)=0 for allv∈ E(G); and (ii) If A=E(G) and A⊆V(Q_1 (G)), then d_A (v)=0 if v∈V(G) and d_A (v) = d_(Q_1 (G) ) (v) for all v∈ E(G). Where Q_1 (G)is the 1–quasitotal graph of G and d_A (v) is the degree of vertex v with respect to the given vertex set A.

Satyanarayana Bhavanari, Srinivasulu Devanaboina, Mallikarjun Bhavanari and Eswaraiah Setty Sriramula
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Int J Inf Res Rev
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