منابع مشابه
Valency of Distance-regular Antipodal Graphs with Diameter 4
Let G be a non-bipartite strongly regular graph on n vertices of valency k. We prove that if G has a distance-regular antipodal cover of diameter 4, then k ≤ 2(n + 1)/5 , unless G is the complement of triangular graph T (7), the folded Johnson graph J (8, 4) or the folded halved 8-cube. However, for these three graphs the bound k ≤ (n − 1)/2 holds. This result implies that only one of a complem...
متن کاملDiameter of 4-colourable graphs
We prove that for every connected 4-colourable graph G of order n and minimum degree δ ≥ 1, diam(G) ≤ 5n 2δ − 1. This is a first step toward proving a conjecture of Erdős, Pach, Pollack and Tuza [4] from 1989.
متن کاملAntipodal Embeddings of Graphs
An antipodal graph D of diameter d has the property that each vertex v has a unique (antipodal) vertex v at distance d from v in D. We show that any such D has circuits of length Id passing through antipodal pairs of vertices. The identification of antipodal vertex-pairs in D produces a quotient graph G with a double cover projection morphism p : D-+G. Using the two-fold quotient map of surface...
متن کاملAntipodal Bipolar Fuzzy Graphs
The concept of an antipodal bipolar fuzzy graph of a given bipolar fuzzy graph is introduced. Characterizations of antipodal bipolar fuzzy graphs are presented when the bipolar fuzzy graph is complete or strong. Some isomorphic properties of antipodal bipolar fuzzy graph are discussed. The notion of self median bipolar fuzzy graphs of a given bipolar fuzzy graph is also introduced.
متن کاملOn Diameter of Line Graphs
The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mohyla Mathematical Journal
سال: 2018
ISSN: 2617-7080
DOI: 10.18523/2617-7080i2018p34-37