scholarly journals A recursive characterization of the 4-connected graphs

1990 ◽  
Vol 84 (1) ◽  
pp. 105-108 ◽  
Author(s):  
Nicola Martinov
Keyword(s):  
Connected Graphs

A constructive characterization of contraction critical 8-connected graphs with minimum degree 9

2019 ◽  
Vol 342 (11) ◽  
pp. 3047-3056
Author(s):  
Chengfu Qin ◽  
Weihua He ◽  
Kiyoshi Ando
Keyword(s):  
Minimum Degree ◽  
Connected Graphs

scholarly journals Graphs with Constant Sum of Domination and Inverse Domination Numbers

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
T. Tamizh Chelvam ◽  
T. Asir
Keyword(s):  
Minimum Degree ◽  
Dominating Set ◽  
Domination Number ◽  
Complete Characterization ◽  
Dominating Sets ◽  
Minimum Cardinality ◽  
Connected Graphs ◽  
Vertex Set ◽  
Domination Numbers

A subset D of the vertex set of a graph G, is a dominating set if every vertex in V−D is adjacent to at least one vertex in D. The domination number γ(G) is the minimum cardinality of a dominating set of G. A subset of V−D, which is also a dominating set of G is called an inverse dominating set of G with respect to D. The inverse domination number γ′(G) is the minimum cardinality of the inverse dominating sets. Domke et al. (2004) characterized connected graphs G with γ(G)+γ′(G)=n, where n is the number of vertices in G. It is the purpose of this paper to give a complete characterization of graphs G with minimum degree at least two and γ(G)+γ′(G)=n−1.

A characterization of weakly four-connected graphs

2006 ◽  
Vol 52 (3) ◽  
pp. 217-229 ◽  
Author(s):  
Tibor Jordán
Keyword(s):  
Connected Graphs

scholarly journals The characterization of graphs with eigenvalue -1 of multiplicity n-4 or n-5

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5919-5933
Author(s):  
Yuhong Yang ◽  
Qiongxiang Huang
Keyword(s):  
Connected Graphs ◽  
Minimal Graphs ◽  
B 52

Petrovic in [M. Petrovic, On graphs with exactly one eigenvalue less than -1, J. Combin. Theory Ser. B 52 (1991) 102-112] determined all connected graphs with exactly one eigenvalue less than -1 and all minimal graphs with exactly two eigenvalues less than -1. By using these minimal graphs, in this paper, we determine all connected graphs having ??1 as an eigenvalue with multiplicity n-4 or n-5.

ON THE MINIMAL DISTANCE SPECTRAL RADIUS IN THE CLASS OF BICYCLIC GRAPHS

2014 ◽  
Vol 06 (01) ◽  
pp. 1450014 ◽  
Author(s):  
MILAN NATH ◽  
SOMNATH PAUL
Keyword(s):  
Spectral Radius ◽  
Complete Characterization ◽  
Minimal Distance ◽  
Connected Graphs ◽  
Bicyclic Graphs

Bicyclic graphs are connected graphs in which the number of edges equals the number of vertices plus one. The class of bicyclic graphs of order n, denoted by ℬn, can be partitioned into two subclasses: the class [Formula: see text] of graphs which contain induced ∞-graphs, and the class [Formula: see text] of graphs which contain induced θ-graphs. Bose et al. [2] have found the graph having the minimal distance spectral radius in [Formula: see text]. In this paper, we determine the graphs having the minimal distance spectral radius in [Formula: see text]. These results together give a complete characterization of the graphs having the minimal distance spectral radius in ℬn.

ON THE EXTENSION OF SHARKOVSKIĬ'S THEOREM TO CONNECTED GRAPHS WITH NON-POSITIVE EULER CHARACTERISTIC

1995 ◽  
Vol 05 (05) ◽  
pp. 1395-1405 ◽  
Author(s):  
J. LLIBRE ◽  
J. PARAÑOS ◽  
J. A. RODRIGUEZ
Keyword(s):  
Euler Characteristic ◽  
Topological Graph ◽  
Topological Graphs ◽  
Connected Graphs ◽  
Linear Orderings ◽  
Branching Points ◽  
Branching Point

This paper contains a characterization of all possible sets of periods for all continuous self-maps on a connected topological graph with zero Euler characteristic having all branching points fixed. A characterization in terms of linear orderings is given for the simplest connected topological graph with zero Euler characteristic that has a branching point, the topological graph shaped like the letter σ. In this case a proof follows by lifting the continuous self-map on σ. We show the difficulties that arise in the simplest connected topological graphs with negative Euler characteristic, like for instance the topological graph shaped like the figure 8.

Characterization of minimally -connected graphs

2011 ◽  
Vol 111 (23-24) ◽  
pp. 1124-1129 ◽  
Author(s):  
Xiaofeng Gu ◽  
Hong-Jian Lai ◽  
Senmei Yao
Keyword(s):  
Connected Graphs

scholarly journals On the structure of graphs with path-width at most two

2012 ◽  
Vol 49 (2) ◽  
pp. 211-222 ◽  
Author(s):  
János Barát ◽  
Péter Hajnal ◽  
Yixun Lin ◽  
Aifeng Yang
Keyword(s):  
Structural Properties ◽  
Building Blocks ◽  
Computer Search ◽  
Connected Graphs ◽  
Excluded Minor ◽  
Graph Class

Kinnersley and Langston used a computer search to characterize the class of graphs with path-width at most two. The excluded minor list consists of 110 graphs. This set is fairly large, and the list gives little insight to structural properties of the targeted graph class. We take a different route here. We concentrate on the building blocks of the graphs with path-width at most two and how they are glued together. In this way, we get a short and compact characterization of 2-connected and 2-edge-connected graphs with path-width at most two.

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