Equality co-neighborhood domination in graphs

2021 ◽  
pp. 2150098
Author(s):  
Ahmed A. Omran ◽  
Manal N. Al-Harere ◽  
Sahib Sh. Kahat
Keyword(s):  
Bipartite Graphs ◽  
The Third ◽  
Graph Operations ◽  
New Type ◽  
Complete Bipartite Graphs ◽  
Domination In Graphs ◽  
Complete Path

In this work, a new domination parameter is introduced in the graphs, which is called “equality co-neighborhood”. Various types of properties of this parameter have been studied. Additionally, this parameter has been determined for certain graphs, such as complete, path, cycle, wheel, star, and complete bipartite graphs. In addition, three types of graph operations have been discussed with some properties presented for the new type of domination. The first operation is a complement of the graph especially to the charts mentioned above. The second operation is the union of two graphs, and the third operation is the corona of two graphs.

scholarly journals On acyclic edge-coloring of complete bipartite graphs

2017 ◽  
Vol 340 (3) ◽  
pp. 481-493
Author(s):  
Ayineedi Venkateswarlu ◽  
Santanu Sarkar ◽  
Sai Mali Ananthanarayanan
Keyword(s):  
Edge Coloring ◽  
Bipartite Graphs ◽  
Acyclic Edge Coloring ◽  
Complete Bipartite Graphs

scholarly journals On randomly 3-axial graphs

1982 ◽  
Vol 25 (2) ◽  
pp. 187-206
Author(s):  
Yousef Alavi ◽  
Sabra S. Anderson ◽  
Gary Chartrand ◽  
S.F. Kapoor
Keyword(s):  
Bipartite Graphs ◽  
Disjoint Paths ◽  
Complete Graphs ◽  
Initial Vertex ◽  
Complete Bipartite Graphs

A graph G, every vertex of which has degree at least three, is randomly 3-axial if for each vertex v of G, any ordered collection of three paths in G of length one with initial vertex v can be cyclically randomly extended to produce three internally disjoint paths which contain all the vertices of G. Randomly 3-axial graphs of order p > 4 are characterized for p ≢ 1 (mod 3), and are shown to be either complete graphs or certain regular complete bipartite graphs.

ON MOSTAR INDEX OF GRAPHS

2021 ◽  
Vol 10 (4) ◽  
pp. 2115-2129
Author(s):  
P. Kandan ◽  
S. Subramanian
Keyword(s):  
Connected Graph ◽  
Cartesian Product ◽  
Bipartite Graphs ◽  
Topological Indices ◽  
Great Success ◽  
Complete Graphs ◽  
Molecular Graphs ◽  
Graphs And Networks ◽  
Complete Bipartite Graphs ◽  
Simple Connected Graph

On the great success of bond-additive topological indices like Szeged, Padmakar-Ivan, Zagreb, and irregularity measures, yet another index, the Mostar index, has been introduced recently as a peripherality measure in molecular graphs and networks. For a connected graph G, the Mostar index is defined as $$M_{o}(G)=\displaystyle{\sum\limits_{e=gh\epsilon E(G)}}C(gh),$$ where $C(gh) \,=\,\left|n_{g}(e)-n_{h}(e)\right|$ be the contribution of edge $uv$ and $n_{g}(e)$ denotes the number of vertices of $G$ lying closer to vertex $g$ than to vertex $h$ ($n_{h}(e)$ define similarly). In this paper, we prove a general form of the results obtained by $Do\check{s}li\acute{c}$ et al.\cite{18} for compute the Mostar index to the Cartesian product of two simple connected graph. Using this result, we have derived the Cartesian product of paths, cycles, complete bipartite graphs, complete graphs and to some molecular graphs.

On the Decomposition of Graphs into Complete Bipartite Graphs

2007 ◽  
Vol 23 (3) ◽  
pp. 255-262 ◽  
Author(s):  
Jinquan Dong ◽  
Yanpei Liu
Keyword(s):  
Bipartite Graphs ◽  
Complete Bipartite Graphs

scholarly journals Regular embeddings of complete bipartite graphs

2002 ◽  
Vol 258 (1-3) ◽  
pp. 379-381 ◽  
Author(s):  
Roman Nedela ◽  
Martin Škoviera ◽  
Andrej Zlatoš
Keyword(s):  
Bipartite Graphs ◽  
Complete Bipartite Graphs
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