Star Coloring of Cartesian Product of Paths and Cycles with Complete Bipartite Graphs

2019 ◽  
Vol 10 (6) ◽  
pp. 1332-1340
Author(s):  
P. Hemalatha ◽  
S. N. Subhathraͭ
Keyword(s):  
Cartesian Product ◽  
Bipartite Graphs ◽  
Complete Bipartite Graphs ◽  
Star Coloring

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.

scholarly journals On Cartesian Products of Orthogonal Double Covers

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
R. El Shanawany ◽  
M. Higazy ◽  
A. El Mesady
Keyword(s):  
Cartesian Product ◽  
Bipartite Graphs ◽  
Double Cover ◽  
Cartesian Products ◽  
Double Covers ◽  
Complete Bipartite Graphs ◽  
Orthogonal Double Cover

LetHbe a graph onnvertices and𝒢a collection ofnsubgraphs ofH, one for each vertex, where𝒢is an orthogonal double cover (ODC) ofHif every edge ofHoccurs in exactly two members of𝒢and any two members share an edge whenever the corresponding vertices are adjacent inHand share no edges whenever the corresponding vertices are nonadjacent inH. In this paper, we are concerned with the Cartesian product of symmetric starter vectors of orthogonal double covers of the complete bipartite graphs and using this method to construct ODCs by new disjoint unions of complete bipartite graphs.

scholarly journals On star coloring of Mycielskians

2018 ◽  
Vol 2 (2) ◽  
pp. 82
Author(s):  
K. Kaliraj ◽  
V. Kowsalya ◽  
Vernold Vivin
Keyword(s):  
Chromatic Number ◽  
Graph Transformation ◽  
Clique Number ◽  
Bipartite Graphs ◽  
Complete Graphs ◽  
Chromatic Numbers ◽  
Complete Bipartite Graphs ◽  
Star Coloring

<p>In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph <span class="math"><em>G</em></span> into a new graph <span class="math"><em>μ</em>(<em>G</em>)</span>, we now call the Mycielskian of <span class="math"><em>G</em></span>, which has the same clique number as <span class="math"><em>G</em></span> and whose chromatic number equals <span class="math"><em>χ</em>(<em>G</em>) + 1</span>. In this paper, we find the star chromatic number for the Mycielskian graph of complete graphs, paths, cycles and complete bipartite graphs.</p>

scholarly journals Number of Spanning Trees of Different Products of Complete and Complete Bipartite Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-23 ◽  
Author(s):  
S. N. Daoud
Keyword(s):  
Tensor Product ◽  
Linear Algebra ◽  
Spanning Trees ◽  
Matrix Theory ◽  
Cartesian Product ◽  
Bipartite Graphs ◽  
Normal Product ◽  
Complete Bipartite Graphs ◽  
Composition Product ◽  
Number Of Spanning Trees

Spanning trees have been found to be structures of paramount importance in both theoretical and practical problems. In this paper we derive new formulas for the complexity, number of spanning trees, of some products of complete and complete bipartite graphs such as Cartesian product, normal product, composition product, tensor product, symmetric product, and strong sum, using linear algebra and matrix theory techniques.

scholarly journals Complexity of Products of Some Complete and Complete Bipartite Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-25 ◽  
Author(s):  
S. N. Daoud
Keyword(s):  
Tensor Product ◽  
Spanning Trees ◽  
Cartesian Product ◽  
Bipartite Graphs ◽  
Matrix Analysis ◽  
Normal Product ◽  
Analysis Techniques ◽  
Complete Bipartite Graphs ◽  
Composition Product ◽  
Number Of Spanning Trees

The number of spanning trees in graphs (networks) is an important invariant; it is also an important measure of reliability of a network. In this paper, we derive simple formulas of the complexity, number of spanning trees, of products of some complete and complete bipartite graphs such as cartesian product, normal product, composition product, tensor product, and symmetric product, using linear algebra and matrix analysis techniques.

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
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