Neighbors degree sum energy of graphs

2021 ◽  
Author(s):  
H. S. Boregowda ◽  
R. B. Jummannaver
Keyword(s):  
Degree Sum

scholarly journals Degree and neighborhood intersection conditions restricted to induced subgraphs ensuring Hamiltonicity of graphs

2014 ◽  
Vol 06 (03) ◽  
pp. 1450043
Author(s):  
Bo Ning ◽  
Shenggui Zhang ◽  
Bing Chen
Keyword(s):  
Hamilton Cycles ◽  
Induced Subgraphs ◽  
Degree Sum ◽  
Degree Condition

Let claw be the graph K1,3. A graph G on n ≥ 3 vertices is called o-heavy if each induced claw of G has a pair of end-vertices with degree sum at least n, and called 1-heavy if at least one end-vertex of each induced claw of G has degree at least n/2. In this note, we show that every 2-connected o-heavy or 3-connected 1-heavy graph is Hamiltonian if we restrict Fan-type degree condition or neighborhood intersection condition to certain pairs of vertices in some small induced subgraphs of the graph. Our results improve or extend previous results of Broersma et al., Chen et al., Fan, Goodman and Hedetniemi, Gould and Jacobson, and Shi on the existence of Hamilton cycles in graphs.

scholarly journals Nonhamiltonian 2-connected claw-free graphs with large 4-degree sum

2001 ◽  
Vol 236 (1-3) ◽  
pp. 123-130 ◽  
Author(s):  
Wacław Frydrych
Keyword(s):  
Degree Sum

scholarly journals Degree sum conditions for the circumference of 4-connected graphs

2014 ◽  
Vol 333 ◽  
pp. 66-83
Author(s):  
Shuya Chiba ◽  
Masao Tsugaki ◽  
Tomoki Yamashita
Keyword(s):  
Connected Graphs ◽  
Degree Sum

GENERA OF THE LINKS DERIVED FROM 2-CONNECTED PLANE GRAPHS

2012 ◽  
Vol 21 (14) ◽  
pp. 1250129 ◽  
Author(s):  
SHUYA LIU ◽  
HEPING ZHANG
Keyword(s):  
Explicit Formula ◽  
Large Family ◽  
Plane Graph ◽  
Plane Graphs ◽  
Degree Sum ◽  
Oriented Link

In this paper, we associate a plane graph G with an oriented link by replacing each vertex of G with a special oriented n-tangle diagram. It is shown that such an oriented link has the minimum genus over all orientations of its unoriented version if its associated plane graph G is 2-connected. As a result, the genera of a large family of unoriented links are determined by an explicit formula in terms of their component numbers and the degree sum of their associated plane graphs.

Some Results on Degree Sum Energy of a Graph

2020 ◽  
pp. 353-359
Author(s):  
Mitesh J. Patel ◽  
G. V. Ghodasara
Keyword(s):  
Degree Sum

On a Sharp Degree Sum Condition for Disjoint Chorded Cycles in Graphs

2010 ◽  
Vol 26 (2) ◽  
pp. 173-186 ◽  
Author(s):  
Shuya Chiba ◽  
Shinya Fujita ◽  
Yunshu Gao ◽  
Guojun Li
Keyword(s):  
Degree Sum ◽  
Chorded Cycles ◽  
Degree Sum Condition

scholarly journals Degree Sum Exponent Distance Energy of Some Graphs

2021 ◽  
Vol 27 (1) ◽  
pp. 64-74
Author(s):  
Jeetendra Gurjar ◽  
Sudhir Raghunath Jog
Keyword(s):  
Distance Matrix ◽  
Degree Sum ◽  
Square Matrix

The degree sum exponent distance matrix M(G)of a graph G is a square matrix whose (i,j)-th entry is (di+dj)^ d(ij) whenever i not equal to j, otherwise it is zero, where di is the degree of i-th vertex of G and d(ij)=d(vi,vj) is distance between vi and vj. In this paper, we define degree sum exponent distance energy E(G) as sum of absolute eigenvalues of M(G). Also, we obtain some bounds on the degree sum exponent distance energy of some graphs and deduce direct  expressions for some graphs.

Degree sum and vertex dominating paths

2018 ◽  
Vol 89 (3) ◽  
pp. 250-265
Author(s):  
Jill Faudree ◽  
Ralph J. Faudree ◽  
Ronald J. Gould ◽  
Paul Horn ◽  
Michael S. Jacobson
Keyword(s):  
Degree Sum

Identifying and ranking influential spreaders in complex networks by combining a local-degree sum and the clustering coefficient

2018 ◽  
Vol 32 (06) ◽  
pp. 1850118 ◽  
Author(s):  
Mengtian Li ◽  
Ruisheng Zhang ◽  
Rongjing Hu ◽  
Fan Yang ◽  
Yabing Yao ◽  
...  
Keyword(s):  
Complex Networks ◽  
Nearest Neighbors ◽  
Sir Model ◽  
Clustering Coefficient ◽  
Degree Centrality ◽  
Competitive Performance ◽  
Spreading Process ◽  
Degree Sum ◽  
Local Degree ◽  
Crucial Problem

Identifying influential spreaders is a crucial problem that can help authorities to control the spreading process in complex networks. Based on the classical degree centrality (DC), several improved measures have been presented. However, these measures cannot rank spreaders accurately. In this paper, we first calculate the sum of the degrees of the nearest neighbors of a given node, and based on the calculated sum, a novel centrality named clustered local-degree (CLD) is proposed, which combines the sum and the clustering coefficients of nodes to rank spreaders. By assuming that the spreading process in networks follows the susceptible–infectious–recovered (SIR) model, we perform extensive simulations on a series of real networks to compare the performances between the CLD centrality and other six measures. The results show that the CLD centrality has a competitive performance in distinguishing the spreading ability of nodes, and exposes the best performance to identify influential spreaders accurately.

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