Cactus Graphs with Cycle Blocks and Square Product Labeling

A graph G is known to be square product labeling, if there exists a bijection f from V (G) to {1, 2, 3,..., p} which induces f* from E(G) to N, defined by f*(uv) = f(u)^2 f(v)^2 is injective for each uv in E(G), for which the labeling pattern of edges are distinct. G is considered to be square product graph, if it admits a square product labeling. In this article, the results are obtained on square product labeling for some cactus graphs with cycle blocks

Square Sum And Square Difference Labelings Of Semitotal-block Graph For Some Class Of Graphs

A graph G is said to be square sum and square difference labeling, if there exists a bijection f from V (G) to {1, 2, 3, ..., (p − 1)} which induces the injective function f ∗ from E(G) to N, defined by f ∗(uv) = f(u)2 + f(v)2 and f ∗(uv) = f(u)2 − f(v)2 respectively, for each uv ∈ E(G) and the resulting edges are distinctly labeled. G is said to be square sum and square difference graph, if it asdmits a square sum and square difference labeling respectively. The present work investigates, square sum and square difference labelingof semitotal-block graph for some class of graphs which are proved using number theory concept

On the planarity of line Mycielskian graph of a graph

The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤  i ≤  q and e, then for 1 ≤  i ≤  q , joining ei' to the neighbours of ei  and  to e. The vertex e is called the root of Lμ(G).  This research paper deals with the characterization of planarity of line Mycielskian Graph Lμ(G) of a graph. Further, we also obtain the characterization on outerplanar, maximal planar, maximal outerplanar, minimally nonouterplanar and 1-planar of Lμ(G).Keywords :  Planar graph, Outerplanar, Maximal planar, Maximal outerplanar, Minimally nonouterplanar and 1-planar.2010 AMS subject classifications : 05C07, 05C10, 05C38, 05C60, 05C76

Distance Based Topological Indices of Double graphs and Strong Double graphs

Topological index is a numerical representation of structure of graph. They are mainly classified as Distance and Degree based topological indices. In this article Distance based topological indices of Double graphs and Strong Double graphs are calculated. Let $G$ be a graph of order $n$ with the vertex set $V(G)$ containing vertices $v_1,v_2,....,v_n$. Double graph of graph $G$ is constructed by taking two copies of G in which a vertex $v_i$ in one copy is adjacent to a vertex $v_j$ in the another copy if $v_i$ and $v_j$ are adjacent in G. Strong Double graph is a double graph in which a vertex $v_i$ in one copy is adjacent to a vertex $v_j$ in the another copy if $i=j$.

Cactus Graphs with Cycle Blocks and Square Product Labeling

In many real world problems, cactus graphs were considered as models from both algorithmic and theoretical point of view and this graph is a subclass of planar graph and superclass of a tree. In this article, the study has been carried out on some cactus graphs with cycle blocks for obtaining results on square product labeling

Distance Based Topological Indices of Double graphs and Strong Double graphs

Topological index is a numerical representation of structure of graph. They are mainly classified as Distance and Degree based topological indices. In this article Distance based topological indices of Double graphs and Strong Double graphs are calculated. Let $G$ be a graph of order $n$ with the vertex set $V(G)$ containing vertices $v_1,v_2,....,v_n$. Double graph of graph $G$ is constructed by taking two copies of G in which a vertex $v_i$ in one copy is adjacent to a vertex $v_j$ in the another copy if $v_i$ and $v_j$ are adjacent in G. Strong Double graph is a double graph in which a vertex $v_i$ in one copy is adjacent to a vertex $v_j$ in the another copy if $i=j$

Book of Abstracts of the 2nd International Conference on Applied Mathematics and Computational Sciences (ICAMCS-2022)

It is a great privilege for us to present the abstract book of ICAMCS-2022 to the authors and the delegates of the event. We hope that you will find it useful, valuable, aspiring, and inspiring. This book is a record of abstracts of the keynote talks, invited talks, and papers presented by the participants, which indicates the progress and state of development in research at the time of writing the research article. It is an invaluable asset to all researchers. The book provides a permanent record of this asset. Conference Title: 2nd International Conference on Applied Mathematics and Computational SciencesConference Acronym: ICAMCS-2022Conference Date: 12-14 October 2022Conference Organizers: DIT University, Dehradun, IndiaConference Mode: Online (Virtual