Comparison of catalog of (3, g) Hamiltonian bipartite graphs with other known lists
نویسنده
چکیده
The focus of this paper is on discussion of a catalog of a class of (3, g) graphs for even girth g. A (k, g) graph is a graph with regular degree k and girth g. This catalog is compared with other known lists of (3, g) graphs such as the enumerations of trivalent symmetric graphs and enumerations of trivalent vertex-transitive graphs, to conclude that this catalog has graphs for more orders than these lists. This catalag also specifies a list of orders, rotational symmetry and girth for which the class of (3, g) graphs do not exist. It is also shown that this catalog of graphs extends infintely.
منابع مشابه
About the catalog of (3, g) Hamiltonian bipartite graphs
A catalog of a class of (3, g) graphs for even girth g is introduced in this paper. A (k, g) graph is a graph with regular degree k and girth g. This catalog of (3, g) graphs for even girth g satisfying 6 ≤ g ≤ 16, has the following properties. Firstly, this catalog contains the smallest known (3, g) graphs. An appropriate class of trivalent graphs for this catalog has been identified, such tha...
متن کاملBalanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations
A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...
متن کاملThe distinguishing chromatic number of bipartite graphs of girth at least six
The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The distinguishing chromatic number $chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum ...
متن کاملThe p-median and p-center Problems on Bipartite Graphs
Let $G$ be a bipartite graph. In this paper we consider the two kind of location problems namely $p$-center and $p$-median problems on bipartite graphs. The $p$-center and $p$-median problems asks to find a subset of vertices of cardinality $p$, so that respectively the maximum and sum of the distances from this set to all other vertices in $G$ is minimized. For each case we present some proper...
متن کاملMixed cycle-E-super magic decomposition of complete bipartite graphs
An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) + ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1601.02887 شماره
صفحات -
تاریخ انتشار 2015