http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
On the first Zagreb index and multiplicative Zagreb coindices of graphs
Das, Kinkar Ch.,Akgunes, Nihat,Togan, Muge,Yurttas, Aysun,Cangul, I. Naci,Cevik, A. Sinan De Gruyter Open 2016 Analele Stiintifice ale Universitatii Ovidius Cons Vol.24 No.1
<P>For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M-1(G) = Sigma v(i is an element of V(G))d(C)(v(i))(2), where d(G) (v(i)) is the degree of vertex v(i), in G. Recently Xu et al. introduced two graphical invariants (Pi) over bar (1) (G) = Pi v(i)v(j is an element of E(G)) (dG (v(i))+dG (v(j))) and (Pi) over bar (2)(G) = Pi(vivj is an element of E(G)) (dG (v(i))+dG (v(j))) named as first multiplicative Zagreb coindex and second multiplicative Zagreb coindex, respectively. The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G, that is, NK(G) = Pi(n)(i=1) d(G) (v(i)). The irregularity index t(G) of G is defined as the num=1 ber of distinct terms in the degree sequence of G. In this paper, we give some lower and upper bounds on the first Zagreb index M-1(G) of graphs and trees in terms of number of vertices, irregularity index, maximum degree, and characterize the extremal graphs. Moreover, we obtain some lower and upper bounds on the (first and second) multiplicative Zagreb coindices of graphs and characterize the extremal graphs. Finally, we present some relations between first Zagreb index and NarumiKatayama index, and (first and second) multiplicative Zagreb index and coindices of graphs.</P>
The number of representations of positive integers by positive quadratic forms
A. Tekcan,O. Bizim,I. Cangül 장전수학회 2006 Proceedings of the Jangjeon mathematical society Vol.9 No.2
In this paper, we consider the number of representations of pos- itive integers by direct sum of binary quadratic forms F1(x1; y1) = x2 1 + 3x1x2 + 8x2 2 and G1(x1; y1) = 2x2 1 + 3x1x2 + 4x2 2 of discriminant ¡23. We derived some results concerning the modular forms }(¿; Q; 'rs) and their or- ders ord (}(¿; Q; 'rs); i1; ¡0(23)), where Q (Q = F2;G2; F1 ©G1; direct sum of F1 and G1) is the positive de¯nite quadratic form and 'rs is the spherical function of second order with respect to Q. We constructed a basis for the cusp form space S4(¡0(23); 1), and then we obtained some formulas for the number of representations of positive integer n by positive de¯nite quadratic forms F4;G4; F3 © G1; F2 © G2 and F1 © G3 using the elements of the space S4(¡0(23); 1).
ON THE HIGHER-ORDER w-q-GENOCCHI NUMBERS
I. N.. Cangul,H. Ozden,V. Kurt,Y. Simsek 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.1
Main purpose of this paper is to study on higher-order w-q-Genocchi numbers and polynomials by using p-adic q-deformed fermi- onic integral on Zp. We derive some identities related to higher-order w-q- Genocchi numbers and polynomials. We also give interpolation functions of these numbers and polynomials.
GENERALIZATION OF q-APOSTOL-TYPE EULERIAN NUMBERS AND POLYNOMIALS, AND THEIR INTERPOLATION FUNCTIONS
I. N. Cangul,A. S. Cevik,Y. Simsek 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.2
In a recent paper [16], generating functions in terms of non- negative real parameters, q-Eulerian type polynomials and numbers (or q-Apostol type Frobenius-Euler numbers and polynomials) have been constructed by Y. Simsek. Additionally, some identities for these poly- nomials and numbers based on the generating functions and functional equations have been derived. Finally, a multiplication formula for the generalized Apostol type Frobenius-Euler polynomials has been given. In this paper, as a continuing study of [16], we will essentially present generalizations of the above material and, dierently from aforemen- tioned paper, we will express the interpolation functions related to these numbers and polynomials.
Integrity of quasi-total graphs
B. Basavanagoud,P. Jakkannavar,I. N. Cangul 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.4
A communication network can be considered to be highly vulnerable to dis- ruption if the failure of few members can result in no member's being able to communicate with very many others. This idea suggests the concept of the integrity of a graph. The integrity I(G) of a graph G is defined as I(G) = minS⊂V(G){|S|+m(G-S)} where m(G-S)denotes the order of the largest component of G-S. In this paper, we obtain the integrity of quasi-total graph of some standard graph families and combinations of these graphs. Further, we establish some relations connecting the integrity of some graph families and integrity of their quasi-total graphs.
Remarks on q-Bernoulli numbers associated with Daehee numbers
H. Ozden,I. N. Cangul,Y. Simsek 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.18 No.1
In this work, we study on Carlitz's type q-Bernoulli numbers, q-Frobenius-Euler numbers and Daehee numbers and polynomials. We also give p-adic integral representation of the twisted Daehee polynomials. By using this representation, we ¯nd Raabe-type multiplication formula for the twisted Daehee polynomials.
Characteristic polynomials of oriented graphs
P. Mahalank,U. Ana,I. N. Cangul 장전수학회 2023 Proceedings of the Jangjeon mathematical society Vol.26 No.2
Characteristic polynomials of oriented graphs
On the entire ABC index of graphs
A. Saleh,A. Aqeel,I. N. Cangul 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.1
Topological indices are graph invariants computed usually by means of the distances or vertex degrees of molecular graphs. In chemical graph theory, topological indices have been successfully used in describing the structure and also predicting certain physico-chemical properties of chem- ical compounds. Atom-bond connectivity (ABC) index has been applied to the study of the stability of alkanes and to the strain the energy of cycloalkanes. The atom bond connectivity (ABC) index of a graph G is defined as where E(G) denotes the set of edges of G and deg(u) and deg(v) are the degrees of the vertices u and v, respectively. Recently, for several applications, the entire versions of the topological indices are defined and studied. In this versions of the topological indices, not only the vertices or the edges are considered in calculations. Both of them are used instead. In this research, we introduce and study the entire atom bond connectivity index of a graph. Exact values of this index for some families of graphs are obtained and some important properties of this new index are established.
A new cryptographic method by means of Molecular graphs
L. Shobana,J. B. Babujee,I. N. Cangul 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.4
Encryption and decryption, the two steps of cryptography, mostly emerge from mathematics. Both operations are done by means of several mathematical methods making use of number theory, elliptic curves, affine transformations, modular arithmetic, matrices, functions, etc. Graph theory has been in interaction with Chemistry since 1947 when Wiener used a mathematical formula, later called as Wiener index, to compare the boiling points of some alkane isomers. Since than, many mathematical methods have been used to determine the chemical and physical properties of molecular structures. In this work, a new tech- nique has been proposed to encrypt and decrypt a secret message using a topological index of a selected molecular graph to avoid the interference of adversaries.
ON r-DYNAMIC COLORINGS OF THE FRIENDSHIP GRAPH FAMILIES
G. NANDINI,M. Venkatachalam,T. DEEPA,I. N. CANGUL 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.2
Coloring of graphs is an important area in graph theory with numerous applications including the most famous problems related to graphs. An r-dynamic coloring of a graph G is a proper coloring c of the vertices such that |c(N(v))| ≥ min {r, d(v)}, for each vertex v ∈ V (G). The r-dynamic chromatic number of a graph G is the minimum k such that G has an r-dynamic coloring with k colors. In this paper, we obtain the r-dynamic chromatic number of Pn + Fn, Kn + Fn, L(Fn) and central graphs of the friendship graph.