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- 저자 : S. V. Roopa (검색결과 3 건)
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Partition energy of complete product of circulant graphs and some new class of graphs
E. Sampathkumar,S. V. Roopa,K. A. Vidya,M. A. Sriraj 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.2
Let G = (V,E) be a graph and Pk = {V1, V2, ..., Vk} be a partition of V . The L-matrix with respect to a partition Pk of the vertex set V of graph G of order n is the unique square symmetric matrix Pk(G) = [aij ] with zero diagonal, whose entries aij with i 6≠ j are defined as follows: (i) If vi, vj ∈ Vr, then aij = 2 or −1 according as vivj is an edge or not. (ii) If vi ∈ Vr and vj ∈ Vs for r 6≠s, then aij = 1 or 0 according as vivj is an edge or not. For all Vi and Vj in Pk, i 6≠j remove the edges between vertices of Vi and Vj and add the edges between the vertices of Vi and Vj which are not in G, the resulting graph is called k-complement of G and is denoted by (G)k. For each set Vr in Pk, remove the edges of G joining the vertices within Vr and add the edges of G (complement of G) joining the vertices of Vr, the graph obtained is called k(i)-complement and is denoted by (G)k(i). The k-partition energy of a graph G with respect to partition Pk is denoted by EPk (G) and is defined as the sum of the absolute values of k-partition eigenvalues of Pk(G). In this paper we construct some graphs such that the graph and its 2-complement are equienergetic with respect to a given partition. We also determine partition energy of complete product of m copies of a circulant graph G and its subgraph, their k-complement and k(i)-complement.
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E. Sampathkumar,S. V. Roopa,K. A. Vidya,M. A. Sriraj 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.4
Let G = (V,E) be a graph. Let V1, V2, . . . , Vk be non-empty disjoint subsets of V such that union equal to V . Then {V1, V2, . . . , Vk} is called partition of vertex set V . Using this partition the graph G can be uniquely represented by a matrix called L-matrix Pk(G), whose entries belong to the set {2, 1, 0,−1} and defined as follows: aij = 8>>< >>: 2 if vi and vj are adjacent within the partition Vi, −1 if vi and vj are non-adjacent within the partition Vi, 1 if vi and vj are adjacent between the partition Vi and Vj for i 6= j, 0 otherwise. The eigenvalues of this matrix are called k-partition eigenvalues of G. The k-partition energy EPk (G) is defined as the sum of the absolute values of kpartition eigenvalues of G. We determine partition energy of some known graphs and also obtain bounds for EPk (G).
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Partition energy of some lexicographic product of two graphs
M. A. Sriraj,B. C. Shwetha,C. R. Veena,S. V. Roopa 장전수학회 2022 Proceedings of the Jangjeon mathematical society Vol.25 No.4
In this paper, we consider some lexicographic product of two graphs G and H of the form Gm(Hn) and determine its m-partition energy. Also,we determine the partition energy with respect to their m-complement and m(i)-complement.
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