Divisor Degree Energy of Some Graphs using Mat Lab Programme

doi:10.35940/ijeat.a1194.1291s419

Divisor Degree Energy of Some Graphs using Mat Lab Programme

International Journal of Engineering and Advanced Technology - Regular Issue ◽

10.35940/ijeat.a1194.1291s419 ◽

2019 ◽

Vol 9 (1S3) ◽

pp. 400-404

Keyword(s):

Star Graph ◽

Tree Graphs ◽

Splitting Graph ◽

Degree Matrix

In this paper, we find the divisor degree matrix of wheel, fan, complete bipartite and splitting graph of star graph and generate their divisor degree energy. Also, we obtain the divisor degree matrix of a tree graphs such as path, star and comb graph and their divisor degree energy by using MAT LAB programme.

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ON STAR COLORING OF DEGREE SPLITTING OF COMB PRODUCT GRAPHS

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi2002507s ◽

2020 ◽

pp. 507

Author(s):

Ulagammal Subramanian ◽

Vernold Vivin Joseph

Keyword(s):

Chromatic Number ◽

Complete Graph ◽

Vertex Coloring ◽

Star Graph ◽

Path Graph ◽

Product Graphs ◽

Star Coloring ◽

Splitting Graph ◽

Proper Vertex

A star coloring of a graph G is a proper vertex coloring in which every path on four vertices in G is not bicolored. The star chromatic number χs (G) of G is the least number of colors needed to star color G. Let G = (V,E) be a graph with V = S1 [ S2 [ S3 [ . . . [ St [ T where each Si is a set of all vertices of the same degree with at least two elements and T =V (G) − St i=1 Si. The degree splitting graph DS (G) is obtained by adding vertices w1,w2, . . .wt and joining wi to each vertex of Si for 1 i t. The comb product between two graphs G and H, denoted by G ⊲ H, is a graph obtained by taking one copy of G and |V (G)| copies of H and grafting the ith copy of H at the vertex o to the ith vertex of G. In this paper, we give the exact value of star chromatic number of degree splitting of comb product of complete graph with complete graph, complete graph with path, complete graph with cycle, complete graph with star graph, cycle with complete graph, path with complete graph and cycle with path graph.

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FUZZY MAGIC LABELLING OF NEUTROSOPHIC PATH AND STAR GRAPH

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.8.74 ◽

2020 ◽

Vol 9 (8) ◽

pp. 6059-6070

Author(s):

D. Ajay ◽

P. Chellamani

Keyword(s):

Star Graph

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On the Generalized Distance Energy of Graphs

Mathematics ◽

10.3390/math8010017 ◽

2019 ◽

Vol 8 (1) ◽

pp. 17 ◽

Cited By ~ 4

Author(s):

Abdollah Alhevaz ◽

Maryam Baghipur ◽

Hilal A. Ganie ◽

Yilun Shang

Keyword(s):

Lower Bounds ◽

Complete Graph ◽

Connected Graph ◽

Distance Matrix ◽

Wiener Index ◽

Diagonal Matrix ◽

Upper And Lower Bounds ◽

Star Graph ◽

Extremal Graphs ◽

Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

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