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- 저자 : K. N. PRAKASHA (검색결과 4 건)
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Partition Laplacian energy of a graph
K. N. Prakasha,P.Siva Kota Reddy,Ismail Naci CANGUL 장전수학회 2017 Advanced Studies in Contemporary Mathematics Vol.27 No.4
The partition energy of a graph was introduced by E. Sampathkumar et al. in [19] in 2015. In this paper, by the motivation of this new energy, the partition Laplacian energy LEp(G) of a graph is introduced and the LEp(G) of some important graph classes is discussed. Also, we obtain some bounds for the partition Laplacian energy.
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INVERSE SUM INDEG ENERGY OF A GRAPH
P. SIVA KOTA REDDY,K. N. PRAKASHA,Ismail Naci CANGUL 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.1
Let G be a graph with n vertices and let di denote the degree of the vertex vi. For a given graph, there are more than 100 ma- trices obtained by using some properties of the graph. Most important and used ones are the adjacency, incidency and Laplacian matrices. Re- cently, several graph topological indices have been used in dening new graph matrices. Graph energy is the quantity obtained as the sum of the absolute values of all eigenvalues of the adjacency matrix corresponding to the graph. Several types of energy have been dened and applied in dierent applications by means of such graph matrices in place of the adjacency matrix. The inverse sum indeg matrix of a graph G is the n n matrix whose (i; j)-th entry is equal to didj di+dj if the ith and the jth vertices are adjacent and 0 otherwise. The inverse sum indeg energy ISIE(G) of G is similarly dened as the sum of the absolute values of the eigenvalues of the inverse sum indeg matrix. In this paper, we compute the inverse sum indeg characteristic polynomial and the inverse sum indeg energy for standard graphs. Some properties and bounds for ISIE(G) are also obtained.
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K. Srinivasa Rao,K. N. PRAKASHA,KADIRVEL SARAVANAN,Ismail Naci CANGUL 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.1
In this paper, maximum degree energy of graphs is studied. After giving some preliminary new results, bounds for the maximum degree eigenvalues are obtained for a general graph. Also bounds on the maximum degree eigenvalues of some frequently used graph classes are given by means of combinatorial, number theoretical and analysis methods. Many proofs are established by means of some result obtained by Adiga and Smitha. Maximum degree energy is calculated for any given simple graph and also for some classes of graphs and obtained relations with others. Special emphasis is given to unicyclic graphs. Several unicyclic graph classes are dened and their maximum degree eigenvalues and energy are calculated.
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S. VIJAY,K.N PRAKASHA,P.S HEMAVATHI,SMITHA G KINI 장전수학회 2022 Proceedings of the Jangjeon mathematical society Vol.25 No.2
In the midst of 20th century, Ivan Gutman invented the concept of energy of graph which is depends on the numbers 0 (if there is no edge between two vertices) and 1 (If two vertices are adjacent) in adjacency matrix. In the current paper we are introducing a degree based new matrix and energy. We define the matrix as follows (i, j)-entry is equal to ln(di+dj)+e(di+dj ) if i ≠ j and 0 otherwise.(where di, dj be the degree of its ith and jth vertices respectively) In this paper we compute the LE-Degree sum energy for graphs and some graph op- erations. Few important properties and bounds for DSLEE(G) are also discussed.
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