相关论文: The Double Star Sequences and the General Second Z…
We derive an identity connecting any two second-order linear recurrence sequences having the same recurrence relation but whose initial terms may be different. Binomial and ordinary summation identities arising from the identity are…
We study Ihara zeta function for graphs in the context of quivers arising from gauge theories, especially under Seiberg duality transformations. The distribution of poles is studied as we proceed along the duality tree, in light of the weak…
We examine the quantity \[S(G) = \sum_{uv\in E(G)} \min(\text{deg } u, \text{deg } v)\] over sets of graphs with a fixed number of edges. The main result shows the maximum possible value of $S(G)$ is achieved by three different classes of…
We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results provide verifiable conditions ensuring local single-valuedness,…
Let $G$ be a graph of order $n$ and $\mu$ be an adjacency eigenvalue of $G$ with multiplicity $k\geq 1$. A star complement $H$ for $\mu$ in $G$ is an induced subgraph of $G$ of order $n-k$ with no eigenvalue $\mu$, and the vertex subset…
For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the $n$-point functions produced by the topological recursion on these curves via the $n$-point functions…
This paper explores the properties of directed graphs, termed generalized action graphs, which exhibit a strong connection to certain number sequences. Focusing on the structural and combinatorial aspects, we investigate the conditions…
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…
A graph $G$ consists of two parts, the vertices and edges. The vertices constitute the vertex set $V(G)$ and the edges, the edge set. An edge \( e=xy \), \( ev \)-dominates not only the vertices incident to it but also those adjacent to…
In an earlier paper, the authors considered three types of graphs, and three equivalence relations, defined on a group, viz.\ the power graph, enhanced power graph, and commuting graph, and the relations of equality, conjugacy, and same…
This paper is devoted to the study of eigen-sequences for some important operators acting on sequences. Using functional equations involving generating functions, we completely solve the problem of characterizing the fixed sequences for the…
Making use of a majorization technique for a suitable class of graphs, we derive upper and lower bounds for some topological indices depending on the degree sequence over all vertices, namely the first general Zagreb index and the first…
By employing contour integration the derivation of a generalized double finite series involving the Hurwitz-Lerch zeta function is used to derive closed form formulae in terms of special functions. We use this procedure to find special…
An exposition on Spivakovsky's dual graphs of valuations on function fields of dimension two is first given, leading to a proof of minimal generating sequences for the non-divisorial valuations. It should be noted that the definition of…
We prove a general inequality for more than two sequences mirroring that of the discrete two-sequence Cauchy-Schwarz.
A self-contained graph is an infinite graph which is isomorphic to one of its proper induced subgraphs. In this paper, ordinary star-like self-contained graphs are introduced and it is shown that every ordinary star-like self-contained…
In this paper, we define and obtain several properties of the (adjacency) energy of a hypergraph. In particular, bounds for this energy are obtained as functions of structural and spectral parameters, such as Zagreb index and spectral…
We consider the alternating zeta function and the alternating $L$-function of a graph $G$, and express them by using the Ihara zeta function of $G$. Next, we define a generalized alternating zeta function of a graph, and express the…
In this paper we use a contour integral method to derive a generating function in the form of a double series involving the product of two Chebyshev polynomials over generalized independent indices expressed in terms of the incomplete gamma…
The authors Mili$\breve{c}$evi$\acute{c}$ et al. introduced the reformulated Zagreb indices, which is a generalization of classical Zagreb indices of chemical graph theory. In the paper, we characterize the extremal properties of the first…