Author
Şerife Burcu Bozkurt
Bio: Şerife Burcu Bozkurt is an academic researcher. The author has contributed to research in topics: Seidel adjacency matrix & Adjacency list. The author has an hindex of 1, co-authored 3 publications receiving 27 citations.
Papers
More filters
01 Jan 2013
TL;DR: In this paper, sharp upper bounds for the energy and Randic energy of a bipartite graph were established, from which some previously known results could be deduced, and some previously unknown results could also be inferred.
Abstract: Sharp upper bounds for the energy and Randic energy of a (bipartite) graph are established. From these, some previously known results could be deduced.
27 citations
Posted Content•
TL;DR: In this article, the adjacency matrix of one type of graph with 2k (k=1,2,...) vertices was considered and the relationship between one type and well-known Fibonacci sequence was investigated.
Abstract: Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we investigate relationships between one type of graph and well-known Fibonacci sequence. In this content, we consider the adjacency matrix of one type of graph with 2k (k=1,2,...) vertices. It is also known that for any positive integer r, the (i,j)th entry of A^{r} (A is the adjacency matrix of the graph) is just the number of walks from vertex i to vertex j, that use exactly k edges.
Posted Content•
TL;DR: In this paper, a general expression for the entries of the r power of a tridiagonal matrix is given, and the complex factorizations of Fibonacci polynomials and Pell numbers are obtained.
Abstract: In this paper, we obtain a general expression for the entries of the r. (r is integer) power of a certain n-square complex tridiagonal matrix. In addition, we get the complex factorizations of Fibonacci polynomials, Fibonacci and Pell numbers.
Cited by
More filters
TL;DR: This work pursues with this line of research by proving further extremal properties of the degree-based graph entropies by proving their extremal values when considered Shannon entropy- based graph measures.
57 citations
TL;DR: In this article, the energy of the general extended adjacency matrix A = (a i j ) of a simple graph of order n and size m is defined as a i j = F (d i, d j ) if the vertices v i and v j are adjacent, and a I j = 0 otherwise.
41 citations
Posted Content•
TL;DR: This article describes the graphs with minimal ME among all unicyclic and bicyclic graphs with a given diameter d and defines the roots of its matching polynomial.
Abstract: Gutman and Wagner proposed the concept of matching energy (ME) and pointed out that the chemical applications of ME go back to the 1970s. Let $G$ be a simple graph of order $n$ and $\mu_1,\mu_2,\ldots,\mu_n$ be the roots of its matching polynomial. The matching energy of $G$ is defined to be the sum of the absolute values of $\mu_{i}\ (i=1,2,\ldots,n)$. In this paper, we characterize the graphs with minimal matching energy among all unicyclic and bicyclic graphs with a given diameter $d$.
40 citations
TL;DR: The necessary and sufficient conditions for the positive of a mixed graph are presented and the incident matrix and Hermitian Laplacian matrix of a Mixed graph are introduced and some results about the Hermitia LaplACian spectrum are derived.
27 citations
TL;DR: The explicit asymptotic values of Laplacian energies for various lattices are obtained and the various topological indices per vertex of lattice systems are independent of the toroidal, cylindrical, and free boundary conditions.
23 citations