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Papers by Rubul Moran
Advances and applications in discrete mathematics, May 2, 2022
Journal of Molecular Structure
Journal of Mathematical and Computational Science, 2021
For a finite set T of non negative integers containing zero, a function c : V (G) → Z + {0} is sa... more For a finite set T of non negative integers containing zero, a function c : V (G) → Z + {0} is said to be a ST-coloring of the graph G = (V, E), if | c(x) − c(y) | is not in T for any any edge (x, y) and for any two distinct edges (x, y) and (u, v), | c(x) − c(y) | =| c(u) − c(v) |. sp ST (G) is the minimum of the difference between the largest and smallest colors assigned over all the vertices and esp ST (G) is the minimum of the maximum difference between the colors assigned to the vertices of an edge over all the edges of the graph, where the minimum is taken over all ST-coloring c. Here we establish some results related to ST-chromatic number, span and edge span of some graph products namely, Tensor product, Cartesian product and Corona product of graphs.
For a simple undirected graph spread is defined as the difference between the largest and the sma... more For a simple undirected graph spread is defined as the difference between the largest and the smallest eigenvalue of the graph. As 1 is the largest eigenvalue of the Randić matrix therefore disregarding the spectral radius, the Randić spread is the difference between the second largest and the smallest eigenvalue of the Randić matrix. In this communication we have studied the bounds for Randić spread. Moreover we have introduced a new upper and lower bound for this spread.
Theory and Practice of Mathematics and Computer Science Vol. 11, 2021
For a graph G = (V,E) and a finite set T of positive integers containing zero, ST-coloring of a g... more For a graph G = (V,E) and a finite set T of positive integers containing zero, ST-coloring of a graph G is a coloring of the vertices with non negative integers such that for any two vertices of an edge, the absolute differences between the colors of the vertices does not belong to a fixed set T of non negative integers containing zero and for any two distinct edges their absolute differences between the colors of their vertices are distinct. The minimum number of colors needed for an efficient Strong T coloring of a graph is known as ST-Chromatic number. This communication is concerned with the ST-coloring of some non perfect graphs viz. Petersen graph, Double Wheel graph, Helm graph, Flower graph, Sun Flower graph. We compute ST-chromatic number of these non perfect graphs.
Advances and applications in discrete mathematics, May 2, 2022
Journal of Molecular Structure
Journal of Mathematical and Computational Science, 2021
For a finite set T of non negative integers containing zero, a function c : V (G) → Z + {0} is sa... more For a finite set T of non negative integers containing zero, a function c : V (G) → Z + {0} is said to be a ST-coloring of the graph G = (V, E), if | c(x) − c(y) | is not in T for any any edge (x, y) and for any two distinct edges (x, y) and (u, v), | c(x) − c(y) | =| c(u) − c(v) |. sp ST (G) is the minimum of the difference between the largest and smallest colors assigned over all the vertices and esp ST (G) is the minimum of the maximum difference between the colors assigned to the vertices of an edge over all the edges of the graph, where the minimum is taken over all ST-coloring c. Here we establish some results related to ST-chromatic number, span and edge span of some graph products namely, Tensor product, Cartesian product and Corona product of graphs.
For a simple undirected graph spread is defined as the difference between the largest and the sma... more For a simple undirected graph spread is defined as the difference between the largest and the smallest eigenvalue of the graph. As 1 is the largest eigenvalue of the Randić matrix therefore disregarding the spectral radius, the Randić spread is the difference between the second largest and the smallest eigenvalue of the Randić matrix. In this communication we have studied the bounds for Randić spread. Moreover we have introduced a new upper and lower bound for this spread.
Theory and Practice of Mathematics and Computer Science Vol. 11, 2021
For a graph G = (V,E) and a finite set T of positive integers containing zero, ST-coloring of a g... more For a graph G = (V,E) and a finite set T of positive integers containing zero, ST-coloring of a graph G is a coloring of the vertices with non negative integers such that for any two vertices of an edge, the absolute differences between the colors of the vertices does not belong to a fixed set T of non negative integers containing zero and for any two distinct edges their absolute differences between the colors of their vertices are distinct. The minimum number of colors needed for an efficient Strong T coloring of a graph is known as ST-Chromatic number. This communication is concerned with the ST-coloring of some non perfect graphs viz. Petersen graph, Double Wheel graph, Helm graph, Flower graph, Sun Flower graph. We compute ST-chromatic number of these non perfect graphs.