Edge Irregular Reflexive Labeling for the Disjoint Union of Gear Graphs and Prism Graphs
Xiujun Zhang,Muhammad Ibrahim,Syed Ahtsham Ul Haq Bokhary,Muhammad Kamran Siddiqui +3 more
- Vol. 6, Iss: 9, pp 142
TLDR
In this paper, an edge irregular reflexive k-labeling for disjoint association of wheel-related diagrams and deduce the correct estimation of the reflexive edge strength for the m copies of some wheelrelated graphs, specifically gear graphs and prism graphs.Abstract:
In graph theory, a graph is given names—generally a whole number—to edges, vertices, or both in a chart. Formally, given a graph G = ( V , E ) , a vertex naming is a capacity from V to an arrangement of marks. A diagram with such a capacity characterized defined is known as a vertex-marked graph. Similarly, an edge naming is a mapping of an element of E to an arrangement of marks. In this case, the diagram is called an edge-marked graph. We consider an edge irregular reflexive k-labeling for the disjoint association of wheel-related diagrams and deduce the correct estimation of the reflexive edge strength for the disjoint association of m copies of some wheel-related graphs, specifically gear graphs and prism graphs.read more
Citations
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References
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TL;DR: It is established that the irregularity strength of any tree with no vertices of degree two is its number of pendant vertices, which is proportional to the number of vertices in the tree.
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TL;DR: This paper determines the exact value of the total edge irregularity strength of the generalized prism P n m, the Cartesian product C n □ P m of a cycle on n vertices with a path on m vertices.
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On Edge Irregular Total Labeling of Categorical Product of Two Cycles
TL;DR: The exact value of the total edge irregularity strength of the categorical product of two cycles Cn and Cm, for n,m≥3, is determined.