scholarly journals A Note on Connected Six Cyclic Graphs Having Minimum Degree Distance

2021 ◽  
Author(s):  
Nadia Khan ◽  
Fatima Ramazan ◽  
Munazza Shamas
Keyword(s):  
Minimum Degree ◽  
Degree Distance ◽  
Cyclic Graphs

5-Cyclic Graphs with Minimum Degree Distance

2017 ◽  
Vol 6 (3) ◽  
pp. 227-231
Author(s):  
Zia Ullah Khan ◽  
Abdul Hameed ◽  
Gohar Ali ◽  
A. Q. Baig
Keyword(s):  
Minimum Degree ◽  
Degree Distance ◽  
Cyclic Graphs

scholarly journals Minimum Degree Distance of Five Cyclic Graphs

2021 ◽  
Vol 10 (3) ◽  
pp. 84
Author(s):  
Nadia Khan ◽  
Munazza Shamus ◽  
Fauzia Ghulam Hussain ◽  
Mansoor Iqbal
Keyword(s):  
Minimum Degree ◽  
Degree Distance ◽  
Cyclic Graphs

scholarly journals The minimum degree distance of graphs of given order and size

2008 ◽  
Vol 156 (18) ◽  
pp. 3518-3521 ◽  
Author(s):  
Orest Bucicovschi ◽  
Sebastian M. Cioabă
Keyword(s):  
Minimum Degree ◽  
Degree Distance

scholarly journals DEGREE DISTANCE AND MINIMUM DEGREE

2012 ◽  
Vol 87 (2) ◽  
pp. 255-271 ◽  
Author(s):  
S. MUKWEMBI ◽  
S. MUNYIRA
Keyword(s):  
Upper Bound ◽  
Connected Graph ◽  
Minimum Degree ◽  
Degree Of Vertex ◽  
Degree Distance ◽  
Image Position ◽  
Appl Math ◽  
Extremal Properties

AbstractLet G be a finite connected graph of order n, minimum degree δ and diameter d. The degree distance D′(G) of G is defined as ∑ {u,v}⊆V (G)(deg u+deg v) d(u,v), where deg w is the degree of vertex w and d(u,v) denotes the distance between u and v. In this paper, we find an asymptotically sharp upper bound on the degree distance in terms of order, minimum degree and diameter. In particular, we prove that \[ D^\prime (G)\le \frac {1}{4}\,dn\biggl (n-\frac {d}{3}(\delta +1)\biggr )^2+O(n^3). \] As a corollary, we obtain the bound D′ (G)≤n4 /(9(δ+1) )+O(n3) for a graph G of order n and minimum degree δ. This result, apart from improving on a result of Dankelmann et al. [‘On the degree distance of a graph’, Discrete Appl. Math.157 (2009), 2773–2777] for graphs of given order and minimum degree, completely settles a conjecture of Tomescu [‘Some extremal properties of the degree distance of a graph’, Discrete Appl. Math.98(1999), 159–163].

scholarly journals Minimum degree distance among cacti with perfect matchings

2016 ◽  
Vol 205 ◽  
pp. 191-201
Author(s):  
Zhongxun Zhu ◽  
Yunchao Hong
Keyword(s):  
Minimum Degree ◽  
Perfect Matchings ◽  
Degree Distance

A NOTE ON TRICYCLIC GRAPHS WITH MINIMUM DEGREE DISTANCE

2011 ◽  
Vol 03 (01) ◽  
pp. 25-32 ◽  
Author(s):  
WEI ZHU ◽  
SHENGBIAO HU ◽  
HAICHENG MA
Keyword(s):  
Minimum Degree ◽  
Degree Distance ◽  
Tricyclic Graphs

In this paper, we determine all the extremal tricyclic graphs with minimum degree distance.

The Order of Monochromatic Subgraphs with a Given Minimum Degree

10.37236/1725 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Yair Caro ◽  
Raphael Yuster
Keyword(s):  
Positive Integer ◽  
Minimum Degree

Let $G$ be a graph. For a given positive integer $d$, let $f_G(d)$ denote the largest integer $t$ such that in every coloring of the edges of $G$ with two colors there is a monochromatic subgraph with minimum degree at least $d$ and order at least $t$. Let $f_G(d)=0$ in case there is a $2$-coloring of the edges of $G$ with no such monochromatic subgraph. Let $f(n,k,d)$ denote the minimum of $f_G(d)$ where $G$ ranges over all graphs with $n$ vertices and minimum degree at least $k$. In this paper we establish $f(n,k,d)$ whenever $k$ or $n-k$ are fixed, and $n$ is sufficiently large. We also consider the case where more than two colors are allowed.

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