Advances in computer and electrical engineering book series, 2020
Let G=(V(G),E(G)) be a graph. The forgotten topological index of G, denoted F(G), is defined as ∑... more Let G=(V(G),E(G)) be a graph. The forgotten topological index of G, denoted F(G), is defined as ∑v∈V(G) (d(v))3. The second Zagreb index of G, denoted M2(G), is defined as ∑uv∈E(G) d(u)d(v). The hyper-Zagreb index of G, denoted HZ(G), is defined as F(G)+2M2 (G). The authors consider only finite undirected graphs without loops or multiple edges. Lots of theorems have been presented along with related results. Using the hyper-Zagreb index of the complement of a graph, they present sufficient conditions for some properties of the graph.
Journal of Discrete Mathematical Sciences and Cryptography, Dec 1, 2013
Abstract The energy of a graph is defined as the sum of the absolute values of the eigenvalues of... more Abstract The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the graph. The first Zagreb index of a graph is defined as the sum of squares of the degrees of the vertices of the graph. Using energy and the first Zagreb index of the complement of graphs we obtain sufficient conditions for some stable properties of the graphs in this note.
International Journal of Applied Mathematics, Aug 16, 2016
Using the existing upper bounds for the sum of the squares of degrees of graphs, in this note we ... more Using the existing upper bounds for the sum of the squares of degrees of graphs, in this note we present sufficient conditions for stable properties of graphs.
Electronic Journal of Linear Algebra, Feb 21, 2018
In this note, sufficient conditions, based on the largest eigenvalue, are presented for some Hami... more In this note, sufficient conditions, based on the largest eigenvalue, are presented for some Hamiltonian properties of graphs.
Annals of pure and applied mathematics, Dec 31, 2022
In this note, we present sufficient conditions based on the largest eigenvalue of the signless La... more In this note, we present sufficient conditions based on the largest eigenvalue of the signless Laplacian for Hamiltonian and traceable graphs.
Journal of mathematics and informatics, Dec 31, 2022
In this note, we first introduce a new problem called the longest common subsequence and substrin... more In this note, we first introduce a new problem called the longest common subsequence and substring problem. Let X and Y be two strings over an alphabet ∑. The longest common subsequence and substring problem for X and Y is to find the longest string, which is a subsequence of X and a substring of Y. We propose an algorithm to solve the problem.
Let G = (V, E) be a graph. The first Zagreb index and second Zagreb index of G are defined as v∈V... more Let G = (V, E) be a graph. The first Zagreb index and second Zagreb index of G are defined as v∈V d 2 (v) and uv∈E d(u)d(v), respectively. Using first and second Zagreb indices of graphs, we in this note present sufficient conditions for some Hamiltonian properties of graphs.
In this article, sufficient conditions based on the largest eigenvalue, minimum degree, and conne... more In this article, sufficient conditions based on the largest eigenvalue, minimum degree, and connectivity for Hamiltonian and traceable graphs are presented.
In this note, we present sufficient conditions for Hamiltonian cycles in fuzzy graphs. In particu... more In this note, we present sufficient conditions for Hamiltonian cycles in fuzzy graphs. In particular, we extend the well-known Ore's theorem and Dirac's theorem in graph theory to fuzzy graph theory.
The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the grap... more The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the graph. In this note, we present energy conditions for some Hamiltonian properties of graphs.
Using an upper bound for the Laplacian spectral radius of graphs obtained by Shu et al., we in th... more Using an upper bound for the Laplacian spectral radius of graphs obtained by Shu et al., we in this note present su¢ cient conditions which are based on the Laplacian spectral radius for some Hamiltonian properties of graphs.
In this note, we present sufficient conditions for Hamiltonian cycles in fuzzy graphs. In particu... more In this note, we present sufficient conditions for Hamiltonian cycles in fuzzy graphs. In particular, we extend the well-known Ore's theorem and Dirac's theorem in graph theory to fuzzy graph theory.
Let G = (X, Y ; E) be a bipartite graph with two vertex partition subsets X and Y. G is said to b... more Let G = (X, Y ; E) be a bipartite graph with two vertex partition subsets X and Y. G is said to be balanced if |X| = |Y |. G is said to be bipancyclic if it contains cycles of every even length from 4 to |V (G)|. In this note, we present spectral conditions for the bipancyclic bipartite graphs.
Annals of pure and applied mathematics, Dec 31, 2022
Let G be a graph. For a vertex u in G, its 1-degree is defined as the average of the degrees of a... more Let G be a graph. For a vertex u in G, its 1-degree is defined as the average of the degrees of all the vertices which are adjacent to u. The minimum 1-degree of a graph G is defined as the smallest 1-degree among all the 1-degrees of vertices in G. A graph G is triangle-free if no three vertices in G can form a complete graph of order three. In this short note, we present a minimum 1-degree condition for a triangle-free graph to be Hamiltonian.
Advances in computer and electrical engineering book series, 2020
Let G=(V(G),E(G)) be a graph. The forgotten topological index of G, denoted F(G), is defined as ∑... more Let G=(V(G),E(G)) be a graph. The forgotten topological index of G, denoted F(G), is defined as ∑v∈V(G) (d(v))3. The second Zagreb index of G, denoted M2(G), is defined as ∑uv∈E(G) d(u)d(v). The hyper-Zagreb index of G, denoted HZ(G), is defined as F(G)+2M2 (G). The authors consider only finite undirected graphs without loops or multiple edges. Lots of theorems have been presented along with related results. Using the hyper-Zagreb index of the complement of a graph, they present sufficient conditions for some properties of the graph.
Journal of Discrete Mathematical Sciences and Cryptography, Dec 1, 2013
Abstract The energy of a graph is defined as the sum of the absolute values of the eigenvalues of... more Abstract The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the graph. The first Zagreb index of a graph is defined as the sum of squares of the degrees of the vertices of the graph. Using energy and the first Zagreb index of the complement of graphs we obtain sufficient conditions for some stable properties of the graphs in this note.
International Journal of Applied Mathematics, Aug 16, 2016
Using the existing upper bounds for the sum of the squares of degrees of graphs, in this note we ... more Using the existing upper bounds for the sum of the squares of degrees of graphs, in this note we present sufficient conditions for stable properties of graphs.
Electronic Journal of Linear Algebra, Feb 21, 2018
In this note, sufficient conditions, based on the largest eigenvalue, are presented for some Hami... more In this note, sufficient conditions, based on the largest eigenvalue, are presented for some Hamiltonian properties of graphs.
Annals of pure and applied mathematics, Dec 31, 2022
In this note, we present sufficient conditions based on the largest eigenvalue of the signless La... more In this note, we present sufficient conditions based on the largest eigenvalue of the signless Laplacian for Hamiltonian and traceable graphs.
Journal of mathematics and informatics, Dec 31, 2022
In this note, we first introduce a new problem called the longest common subsequence and substrin... more In this note, we first introduce a new problem called the longest common subsequence and substring problem. Let X and Y be two strings over an alphabet ∑. The longest common subsequence and substring problem for X and Y is to find the longest string, which is a subsequence of X and a substring of Y. We propose an algorithm to solve the problem.
Let G = (V, E) be a graph. The first Zagreb index and second Zagreb index of G are defined as v∈V... more Let G = (V, E) be a graph. The first Zagreb index and second Zagreb index of G are defined as v∈V d 2 (v) and uv∈E d(u)d(v), respectively. Using first and second Zagreb indices of graphs, we in this note present sufficient conditions for some Hamiltonian properties of graphs.
In this article, sufficient conditions based on the largest eigenvalue, minimum degree, and conne... more In this article, sufficient conditions based on the largest eigenvalue, minimum degree, and connectivity for Hamiltonian and traceable graphs are presented.
In this note, we present sufficient conditions for Hamiltonian cycles in fuzzy graphs. In particu... more In this note, we present sufficient conditions for Hamiltonian cycles in fuzzy graphs. In particular, we extend the well-known Ore's theorem and Dirac's theorem in graph theory to fuzzy graph theory.
The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the grap... more The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the graph. In this note, we present energy conditions for some Hamiltonian properties of graphs.
Using an upper bound for the Laplacian spectral radius of graphs obtained by Shu et al., we in th... more Using an upper bound for the Laplacian spectral radius of graphs obtained by Shu et al., we in this note present su¢ cient conditions which are based on the Laplacian spectral radius for some Hamiltonian properties of graphs.
In this note, we present sufficient conditions for Hamiltonian cycles in fuzzy graphs. In particu... more In this note, we present sufficient conditions for Hamiltonian cycles in fuzzy graphs. In particular, we extend the well-known Ore's theorem and Dirac's theorem in graph theory to fuzzy graph theory.
Let G = (X, Y ; E) be a bipartite graph with two vertex partition subsets X and Y. G is said to b... more Let G = (X, Y ; E) be a bipartite graph with two vertex partition subsets X and Y. G is said to be balanced if |X| = |Y |. G is said to be bipancyclic if it contains cycles of every even length from 4 to |V (G)|. In this note, we present spectral conditions for the bipancyclic bipartite graphs.
Annals of pure and applied mathematics, Dec 31, 2022
Let G be a graph. For a vertex u in G, its 1-degree is defined as the average of the degrees of a... more Let G be a graph. For a vertex u in G, its 1-degree is defined as the average of the degrees of all the vertices which are adjacent to u. The minimum 1-degree of a graph G is defined as the smallest 1-degree among all the 1-degrees of vertices in G. A graph G is triangle-free if no three vertices in G can form a complete graph of order three. In this short note, we present a minimum 1-degree condition for a triangle-free graph to be Hamiltonian.
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