scholarly journals Distance energy of partial complementary graph

2020 ◽  
Keyword(s):  
Complementary Graph

Approach to spatial modeling of networks and groups of objects on the basis of the weighted graph construction procedure

2020 ◽  
Vol 964 (10) ◽  
pp. 49-58
Author(s):  
V.I. Bilan ◽  
A.N. Grigor’ev ◽  
G.G. Dmitrikov ◽  
E.A. Dudin
Keyword(s):  
Spatial Configuration ◽  
Weighted Graph ◽  
Edge Length ◽  
Buffer Zones ◽  
Typical Structure ◽  
Spatial Graph ◽  
Object Based ◽  
Complementary Graph ◽  
Spatial Parameters ◽  
The Given

The direction of research on the development of a scientific and methodological tool for the analysis of spatial objects in order to determine their generalized spatial parameters was selected. An approach to the problem of modeling networks and groups of objects based on the synthesis of a weighted graph is proposed. The spatial configuration of objects based on the given conditions is described by a weighted graph, the edge length of which is considered as the weight of the edges. A generalization to the typical structure of a spatial graph is formulated; its essence is representation of nodal elements as two-dimensional (polygonal) objects. To take into account the restrictions on the convergence of the vertices described by the buffer zones, a complementary graph is formed. An algorithm for constructing the implementation of a spatial object based on the sequential determination of vertices that comply with the given conditions is proposed. Using the software implementation of the developed algorithm, an experiment was performed to evaluate the spatial parameters of the simulated objects described by typical graph structures. The following parameters were investigated as spatial ones

scholarly journals On Self-Complementary Cyclic Packing of Forests

10.37236/980 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
A.Paweł Wojda ◽  
Mariusz Woźniak ◽  
Irmina A. Zioło
Keyword(s):  
Complementary Graph ◽  
Complementary Permutation

A graph is self-complementary if it is isomorphic to its complement. In this paper we prove that every forest of order $4p$ and size less than $3p$ is a subgraph of a self-complementary graph of order $4p$ with a cyclic self-complementary permutation. We also discuss some generalization of the main result.

scholarly journals Graphs with no induced wheel and no induced antiwheel

2015 ◽  
Vol 9 (2) ◽  
pp. 357-366 ◽  
Author(s):  
Frédéric Maffray
Keyword(s):  
Polynomial Time ◽  
Simple Structure ◽  
Complete Problem ◽  
Complementary Graph ◽  
Np Complete ◽  
Chordless Cycle

A wheel is a graph that consists of a chordless cycle of length at least 4 plus a vertex with at least three neighbors on the cycle. An antiwheel is the complementary graph of a wheel. It was shown recently that detecting induced wheels is an NP-complete problem. In contrast, it is shown here that graphs that contain no wheel and no antiwheel have a very simple structure and consequently can be recognized in polynomial time.

scholarly journals Self-complementary graph decompositions

1992 ◽  
Vol 53 (1) ◽  
pp. 17-24 ◽  
Author(s):  
C. A. Rodger
Keyword(s):  
Graph Decompositions ◽  
Edge Disjoint ◽  
Complementary Graph

AbstractA complementary decomposition of λKn into a graph G is an edge-disjoint decomposition of λKn into copies of G such that if each copy H of G is replaced by its complement in V(H) then the result is an edge-disjoint decomposition of λKn into copies of GC it is a self- complementary decomposition if G = Gc. The spectrum for the last self-complementary graph on at most 7 vertices is found.

scholarly journals Homomorphisms and related contractions of graphs

1988 ◽  
Vol 11 (1) ◽  
pp. 95-100 ◽  
Author(s):  
Robert D. Girse ◽  
Richard A. Gillman
Keyword(s):  
Hadwiger's Conjecture ◽  
Complementary Graph ◽  
Hadwiger’S Conjecture

For every homomorphismϕof a graphGthere exists a contractionθϕonG¯, the complement ofG. Here we study the graph equationϕ(G)=θϕ(G¯). In the course of our work we show that Hadwiger's Conjecture is true for every self-complementary graph.

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