Person: CANGÜL, İSMAİL NACİ
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CANGÜL
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İSMAİL NACİ
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Publication Maximum and minimum degree energies of p -splitting and p -shadow graphs(Turkic World Mathematical Soc, 2022-01-01) Rao, K. S.; Saravanan, K.; Prakasha, K. N.; Cangul, Ismail Naci; CANGÜL, İSMAİL NACİ; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; J-3505-2017Let v(i) and v(j) be two vertices of a graph G. The maximum degree matrix of G is given in [2] byd(ij) = {max{d(i), d(j)} if v(i) and v(j) are adjacent0 otherwise.Similarly the (i, j)-th entry of the minimum degree matrix is defined by taking the minimum degree instead of the maximum degree above, [1]. In this paper, we have elucidated a relation between maximum degree energy of p-shadow graphs with the maximum degree energy of its underlying graph. Similarly, a relation has been derived for minimum degree energy also. We disprove the results E-M(S'(G)) = 2E(M)(G) and E-m(S'(G)) = 2E(m)(G) given by Zheng-Qing Chu et al. [3] by giving some counterexamples.Publication Computing the hosoya and the merrifield-simmons indices of two special benzenoid systems(Univ Kashan, Fac Mathematical Sciences, 2021-06-01) Öz, Mert Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Fen Edebiyat Fakültesi; Matematik Bölümü; J-3505-2017Gutman et al. gave some relations for computing the Hosoya indices of two special benzenoid systems R-n and P-n. In this paper, we compute the Hosoya index and Merrifield-Simmons index of R-n and P-n, by means of introducing four vectors for each benzenoid system and index. As a result, we compute the Hosoya index and the Merrifield-Simmons index of R-n and P-n, by means of a product of a certain matrix of degree n and a certain vector.Publication On the conjecture of jesmanowicz(Centre Environment Social & Economic Research Publ-ceser, 2017-01-01) Togbe, Alain; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Soydan, Gokhan; SOYDAN, GÖKHAN; Demirci, Musa; DEMİRCİ, MUSA; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-0700-5774; 0000-0002-5882-936X; J-3505-2017; A-6557-2018; ABA-6206-2020; M-9459-2017We give a survey on some results covering the last 60 years concerning Jesmanowicz' conjecture. Moreover, we conclude the survey with a new result by showing that the special Diophantine equation(20k)(x) + (99k)(y) = (101k)(z)has no solution other than (x, y, z) = (2, 2, 2).Publication Some notes on randic index(Soc Paranaense Matematica, 2022-01-01) Büyükköse, Şerife; Cangül, Ismail Naci; CANGÜL, İSMAİL NACİ; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0002-0700-5774; J-3505-2017In this paper we establish new inequalities involving Randic index, weigthed Randic index and general Randic index in terms of the eigenvalues, the number of edges, the number of vertices, the energy and vertex degrees.Publication Bounds for the sum of cubes of vertex degrees of splice graphs(Turkic World Mathematical, 2020-01-01) Lokesha, Veerebradiah; Jain, Sushmitha; Muddalapuram, Manjunath; Çevik, Ahmet Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017Some chemically interesting graphs can be derived from simpler graphs by some graph operations. One of the most relevant among these interesting graphs is named as splice graphs. They are related to RNA sequencing and therefore is of great interest. The main target of this paper is to obtain the explicit interpretation of F-index in terms of the graph size and maximum or minimum vertex degrees of special splice graphs.Publication Some graph parameters of power set graphs(Pushpa Publishing House, 2021-03-01) Nacaroğlu, Yaşar; Akgüneş, Nihat; Pak, Sedat; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Fen Edebiyat Fakültesi; Matematik Bölümü; J-3505-2017In this study, we examine some graph parameters such as the edge number, chromatic number, girth, domination number and clique number of power set graphs.Publication Inverse problem for albertson irregularity index(Turkic World Mathematical Soc, 2022-01-01) Güneş, Aysun; YURTTAŞ GÜNEŞ, AYSUN; Togan, M.; Demirci, Musa; DEMİRCİ, MUSA; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0001-5349-3978; 0000-0002-0700-5774; A-6557-2018; AAG-8470-2021; J-3505-2017Graph indices have attracted great interest as they give us numerical clues for several properties of molecules. Some indices give valuable information on the molecules under consideration using mathematical calculations only. For these reasons, the calculation and properties of graph indices have been in the center of research. Naturally, the values taken by a graph index is an important problem called the inverse problem. It requires knowledge about the existence of a graph having index equal to a given number. The inverse problem is studied here for Albertson irregularity index as a part of investigation on irregularity indices. A class of graphs is constructed to show that the Albertson index takes all positive even integers. It has been proven that there exists at least one tree with Albertson index equal to every even positive integer but 4. The existence of a unicyclic graph with irregularity index equal to m is shown for every even positive integer m except 4. It is also shown that the Albertson index of a cyclic graph can attain any even positive integer.Publication A constructive method for the cycloidal normal free subgroups of finite index of hecke groups H (√2) AND H (√3)(Acad Sinica, 2006-09-01) DOĞAN, SETENAY; DEMİRCİ, MUSA; Demirci, Musa; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bizim, Osman; BİZİM, OSMAN; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-0700-5774; A-6557-2018; AAH-1468-2021; AAH-9762-2021; J-3505-2017; ABA-6206-2020Cycloidal subgrups of the modular group are studied in [8]. Here cycloidal free normal subgroups of Hecke groups are considered. It is found that when q equivalent to 2 ( mod 4), H ( lambda(q)) has no such subgroups. In all other cases the signatures of these subgroups are constructed by means of q-gons and their signatures are given.Publication Independence number of graphs and line graphs of trees by means of omega invariant(Springer, 2020-02-26) Srivastava, Gautam; Srivastava, Hari Mohan; Ozden, Hacer; ÖZDEN AYNA, HACER; Zihni, Fikriye Ersoy; Erdogan, Fatma Ozen; ÖZEN ERDOĞAN, FATMA; Cangul, Ismail Naci; CANGÜL, İSMAİL NACİ; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-0700-5774; 0000-0002-3991-0488; AAH-5090-2021; ABA-6206-2020; J-3505-2017; AAG-8274-2021A recently defined graph invariant denoted by O(G) for a graph G is shown to have several applications in graph theory. This number gives direct information on the realizability, number of realizations, connectedness, cyclicness, number of components, chords, loops, pendant edges, faces, bridges, etc. In this paper, we use O to give a characterization of connected unicyclic graphs, to calculate the omega invariant and to formalize the number of faces of the line graph of a tree, and give a new algorithm to formalize the independence number of graphs G and line graphs L(G) by means of the support vertices, pendant vertices and isolated vertices in G.Publication Sum-edge characteristic polynomials of graphs(Taylor & Francis, 2019-01-01) Öz, Mert Sinan; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Yamaç, Çilem; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-0700-5774; ABA-6206-2020Modelling a chemical compound by a (molecular) graph helps us to obtain some required information about the chemical and physical properties of the corresponding molecular structure. Linear algebraic notions and methods are used to obtain several properties of graphs usually by the help of some graph matrices and these studies form an important sub area of Graph Theory called spectral graph theory. In this paper, we deal with the sum-edge matrices defined by means of vertex degrees. We calculate the sum-edge characteristic polynomials of several important graph classes by means of the corresponding sum-edge matrices.