Connected bipancyclic isomorphic m-factorizations of the Cartesian product of graphs
نویسندگان
چکیده
Abstract An m-factorization of a graph is a decomposition of its edge set into edge-disjoint m-regular spanning subgraphs (or factors). In this paper, we prove the existence of an isomorphic m-factorization of the Cartesian product of graphs each of which is decomposable into Hamiltonian even cycles. Moreover, each factor in the m-factorization is m-connected, and bipancyclic for m ≥ 4 and nearly bipancyclic for m = 3.
منابع مشابه
Some results on vertex-edge Wiener polynomials and indices of graphs
The vertex-edge Wiener polynomials of a simple connected graph are defined based on the distances between vertices and edges of that graph. The first derivative of these polynomials at one are called the vertex-edge Wiener indices. In this paper, we express some basic properties of the first and second vertex-edge Wiener polynomials of simple connected graphs and compare the first and second ve...
متن کاملSharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs
In $1994,$ degree distance of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the multiplicative version of degree distance and multiplicative ver...
متن کاملOn the weak reconstruction of Cartesian-product graphs
In this paper we reconstruct nontrivial connected Cartesian product graphs from single vertex deleted subgraphs. We show that all one-vertex extensions of a given connected graph H, nite or innnite, to a nontrivial Cartesian product are isomorphic.
متن کاملUnique Prime Cartesian Factorization of Graphs over Finite Fields
A fundamental result, due to Sabidussi and Vizing, states that every connected graph has a unique prime factorization relative to the Cartesian product; but disconnected graphs are not uniquely prime factorable. This paper describes a system of modular arithmetic on graphs under which both connected and disconnected graphs have unique prime Cartesian factorizations.
متن کاملSecret Sharing Based On Cartesian product Of Graphs
The purpose of this paper is to study the information ratio of perfect secret sharing of product of some special families of graphs. We seek to prove that the information ratio of prism graphs $Y_{n}$ are equal to $frac{7}{4}$ for any $ngeq 5$, and we will gave a partial answer to a question of Csirmaz cite{CL}. We will also study the information ratio of two other families $C_{m}times C_{n}$ a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Australasian J. Combinatorics
دوره 66 شماره
صفحات -
تاریخ انتشار 2016