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Changing relationship between sets using convolution sums of restricted divisor functions
Ismail Naci Cangul,Daeyeoul Kim 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.3
There are real life situations in our lives where the things are changing continuously or from time to time. It is a very important problem for one whether to continue the existing relationship or to form a new one after some occasions. That is, people, companies, cities, countries, etc. may change their opinion or position rapidly. In this work, we think of the problem of changing relationships from a mathematical point of view and think of an answer. In some sense, we comment these changes as power changes. Our number theoretical model will be based on this idea. Using the convolution sum of the restricted divisor function $E$, we obtain the answer to this problem.
SOME RECURRENCE RELATIONS FOR THE ENERGY OF CYCLE AND PATH GRAPHS
FERIHA CELIK,Ismail Naci CANGUL 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.3
Energy of a graph, rst dened by E. Hückel as the sum of absolute values of the eigenvalues of the adjacency matrix while searching for a method to obtain approximate solutions of Schrödinger equation for a class of organic molecules, is an important sub area of graph theory. This equation is a second order dierential equation which include the energy of the corresponding system. The energy of many graph types are well-known in literature. To know the energy of a molecule is an important aspect in Chemical Graph Theory. Two classes, cycles and paths, show serious dierences from others as the eigenvalues are trigonometric algebraic numbers which makes it difficult to calculate the energy of the corresponding graph. Here we obtain the polynomials and recurrence relations for the spectral polynomials of cycles and paths to nd the energy of larger graphs easier than the classical way.
FORGOTTEN INDEX OF GRAPHS WITH DELETED EDGES
PUSHPALATHA MAHALANK,Ismail Naci CANGUL 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.4
The forgotten index F(G) of a graph G is a degree based topological index which is defined as the sum of the cubes of the degrees of its vertices which was introduced by Furtula and Gutman in 2015. It was used in earlier works in relation with the first Zagreb index but not named until 2015. In this work, we present the effect of deleting edges from a simple graph on forgotten index is studied. In particular, some statements for the change of forgotten index of path, cycle, complete, star, complete bipartite and tadpole graphs are obtained. Also the same effect is determined for regular graphs.
MINIMUM PENDANT DOMINATING ESTRADA INDEX OF A GRAPH
AKbar Jahanbani,Ismail Naci CANGUL 장전수학회 2020 Advanced Studies in Contemporary Mathematics Vol.30 No.4
The main purpose of this paper is to introduce the con- cept of minimum pendant dominating Estrada index of a graph. First, we compute minimum pendant dominating Estrada index for complete graph, star graph, complete bipartite graph and cocktail party graph which are amongst the most widely-used graph classes. Also, upper and lower bounds for this new index are established. Finally, the rela- tions between the new Estrada index and the new type of energy are investigated.
Formulae and recurrence relations on spectral polynomials of some graphs
FERIHA CELIK,Ismail Naci CANGUL 장전수학회 2017 Advanced Studies in Contemporary Mathematics Vol.27 No.3
Energy of a graph, firstly defined by E. Hückel as the sum of absolute values of the eigenvalues of the adjacency matrix while searching for a method to obtain approximate solutions of Schrödinger equation for a class of organic molecules, is an important sub area of graph theory. Schrödinger equation is a second order differantial equation which include the energy of the corresponding system. Here we obtain the polynomials and recurrence relations for the spectral (characteristic) polynomials of some graphs.
Bounds for matching number of fundamental realizations according to new graph invariant Omega
MERT SINAN OZ,Ismail Naci CANGUL 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.1
Matching number of a graph is one of the intensively studied areas in graph theory due to numerous applications of the matching and related notions. Recently, Delen and Cangul defined a new graph invariant denoted by which helps to determine several graph theoretical and combinatorial properties of the realizations of a given degree sequence. In this paper, using K2 deletion process, the maximum and minimum matching numbers of all so-called fundamental realizations of a given degree sequence.
RELATIONS BETWEEN THE FIRST AND SECOND ZAGREB INDICES OF SUBDIVISION GRAPHS
Aysun YURTTAS,Muge TOGAN,Ismail Naci CANGUL 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.3
The first and second Zagreb indices of a graph are two of the topological invariants used in molecular calculations by Mathematicians and Chemists. First Zagreb index and multiplicative Zagreb indices, all versions of Zagreb indices of subdivision graphs, Zagreb indices of the line graphs of the subdivision graphs, Zagreb indices of subdivision graphs of double graphs, multiplicative Zagreb indices of graph operations were cal- culated and as a generalisation, the authors determined the multiplicative Zagreb indices of the r-subdivision of double graphs. In this paper, we ob- tain numerous new relations between the first and second Zagreb indices of the subdivision graphs of certain graph types.
K^th-eccentricity index of graphs
Veena Mathad,PARVATHI,Ismail Naci CANGUL 장전수학회 2022 Proceedings of the Jangjeon mathematical society Vol.25 No.2
The molecular topological descriptors are the numerical in- variants of a molecular graph and are very useful for predicting their physical properties, chemical reactivity and bioactivity. A variety of such indices are studied and used in theoretical chemistry and phar- maceutical research related to drugs and also in different fields. The main classes of topological graph indices are those based on vertex de- grees, distances, and graph parameters like eccentricity. In this pa- per, we introduce kth-eccentricity index of graphs. Also we compute kth-eccentricity index of some standard graphs including some wind- mill graphs and molecular graphs of cycloalkenes. Further, we obtain lower and upper bounds for the kth-eccentricity index in terms of other topological indices.
Algebraic Method for Characteristic Edge-Zagreb and Laplacian Polynomials of Graphs
MERT SINAN OZ,Ismail Naci CANGUL 장전수학회 2020 Advanced Studies in Contemporary Mathematics Vol.30 No.3
Polynomials corresponding to graphs and their roots have many applications including the energy defined algebraically by means of the adjacency matrix which is defined as a 0 1 matrix according to the neighbouring relations of vertices. In literature, many notions depend on the adjacency matrix and the characteristic polynomial of the adjacency matrix is used in the definition of the energy of the graph. Recently, some other matrices are used in obtaining characteristic polynomial. In this work, two important matrices, edge-Zagreb and Laplacian, are used to study the characteristic polynomial by means of rather unusual algebraic way of using elementary subgraphs
Inverse problem for the first entire Zagreb index
Muge TOGAN,Aysun YURTTAS,Ismail Naci CANGUL 장전수학회 2019 Advanced Studies in Contemporary Mathematics Vol.29 No.2
The inverse problem for topological graph indices is about the exis- tence of a graph having its index value equal to a given non-negative integer. In this paper, we study the problem for the rst entire Zagreb index. We will rst show that the rst entire Zagreb index must be even for any graph G, and can take all positive even integer values except 4; 6; 10; 12; 14; 18; 20; 22; 26; 28; 30; 36; 38 and 46.