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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.
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).
Bi-efficient domination in graphs
B. Chaluvaraju,K. A. Vidya 장전수학회 2007 Proceedings of the Jangjeon mathematical society Vol.10 No.2
In a graph G = (V, E), a dominating set D ⊆ V is a bi-efficient dominating set of G, if for every vertex u in V, N[u]∩D =2. The bi-efficient domination number of G, denoted by γbe(G) is the minimum cardinality of a bi-efficient dominating set of G. In this paper, many bounds of γbe(G) are obtained and its exact values for some standard graphs are found. Also its relationship with other parameters is investigated.
Bilateral inflammatory cysts of the jaw: report of an unusual case
Holla, Vidya A.,Chatra, Laxmikanth,Shenai, Prashanth,Rao, Prasanna Kumar,Veena, K.M.,Prabhu, Rachana Vishnudas Korean Academy of Oral and Maxillofacial Radiology 2012 Imaging Science in Dentistry Vol.42 No.2
Radicular cyst is the most common odontogenic cyst occurring in the jaws. The cyst is commonly found in relation to the maxillary anterior teeth in the third and fifth decade of life. Although multiple radicular cysts are not uncommon in the jaws, bilaterally symmetrical representation of these cysts is rare. Radiographs prior to extraction help in diagnosis of these cysts and thereby prevent further morbidities. We report a case of 16-year-old male patient who presented bilateral radicular cysts symmetrically in the mandible.
Sathish K.V.,Sridhar K.N.,Seenappa L.,Manjunatha H.C.,Vidya Y.S.,Chinnappa Reddy B.,Manjunatha S.,Santhosh A.N.,Munirathnam R.,Raj Alfred Cecil,Damodara Gupta P.S.,Sankarshan B.M. 한국원자력학회 2023 Nuclear Engineering and Technology Vol.55 No.5
For the first time Aluminium-BariumeZinc oxide nanocomposite (ZABONC) was synthesized by solution combustion method where calcination was carried out at low temperatures (6000 C) to study the electromagnetic (EM) (X/g) radiation shielding properties. Further for characterization purpose standard techniques like PXRD, SEM, UV-VISIBLE, FTIR were used to find phase purity, functional groups, surface morphology, and to do structural analysis and energy band gap determination. The PXRD pattern shows (hkl) planes corresponding to spinel cubic phase of ZnAl2O4, cubic BaðNO3Þ2, a and g phase of Al2O3 which clearly confirms the formation of complex nano composite. From SEM histogram mean size of nano particles was calculated and is in the order of 17 nm. Wood and Tauc’s relation direct energy band gap calculation gives energy gap of 2.9 eV. In addition, EM (X/g) shielding properties were measured and compared with the theoretical ones using standard procedures (NaI (Tl) detector and multi channel analyzer MCA). For energy above 356 keV the measured shielding parameters agree well with the theory, while below this value slight deviation is observed, due to the influence of atomic/crystallite size of the ZABONC. Hence synthesized ZABONC can be used as a shielding material in EM (X/g) radiation shielding