Total Vertex Stress Alteration in Cycle Related Graphs

Acta Universitatis Sapientiae, Informatica, 2021

This paper presents results for some vertex stress related parameters in respect of specific subfamilies of Kneser graphs. Kneser graphs for which diam(KG(n, k)) = 2 and k ≥ 2 are considered. The note establishes the foundation for researching similar results for Kneser graphs for which diam(KG(n, k)) ≥ 3. In addition some important vertex stress related properties are stated. Finally some results for specific bipartite Kneser graphs i.e. BK(n, 1), n ≥ 3 will be presented. In the conclusion some worthy research avenues are proposed.

Canadian Journal of Mathematics, 1967

In this note, G will denote a finite undirected graph without multiple edges, and V = V(G) will denote its vertex set. The largest integer n for which G is n-vertex connected is the vertex-connectivity of G and will be denoted by λ = λ(G). One defines ζ to be the largest integer z not exceeding |V| such that for any set U ⊂ V with |U| = z, there is a cycle in G which contains U. The symbol i(U) will denote the component index of U. As a standard reference for this and other terminology, the authors recommend O. Ore (3).

2007

One of the standard basic steps in drawing hierarchical graphs is to invert some arcs of the given graph to make the graph acyclic. We discuss exact and parameterized algorithms for this problem. In particular we examine a graph class called (1, n)-graphs, which contains cubic graphs. We discuss exact and parameterized algorithms, where we use a non-standard measure approach for the analysis. Especially the analysis of the parameterized algorithm is of special interest, as it is not an amortized analysis modelled by 'finite states' but is rather a 'top-down' amortized analysis. For (1, n)-graphs we achieve a running time of O * (1.1871 m ) and O * (1.212 k ), for cubic graphs O * (1.1798 m ) and O * (1.201 k ), respectively. As a by-product the the trivial bound of 2 n for Feedback Vertex Set on planar directed graphs is broken.

Journal of Ambient Intelligence and Humanized Computing, 2020

A domatic partition of G is the partition of vertices V(G) into disjoint dominating sets. The maximum size of disjoint dominating sets is called the domatic number of G. In this paper, comparative results are investigated on domatic partition of few graphs of cycle related graphs such as complete graph, tadpole graph, lollipop graph and barbell graph for cognitive wireless sensor networks. Then the middle graph and central graph of these graphs are studied and domatic number of the defined graphs are determined to find the nodes in disjoint sets to disribute the tasks uniformly rather than burden the nodes in domatic set. Furthermore, diameter and domination number of these graphs are observed.

Indonesian Journal of Combinatorics, 2021

An edge irregular total k-labeling f : V ∪ E → {1, 2, ..., k} of a graph G = (V, E) is a labeling of vertices and edges of G in such a way that for any two different edges uv and u v , their weights f (u) + f (uv) + f (v) and f (u) + f (u v) + f (v) are distinct.The total edge irregularity strength tes(G) is defined as the minimum k for which the graph G has an edge irregular total k-labeling. In this paper, we determine the total edge irregularity strength of new classes of graphs C m @C n , P * m,n and C * m,n and hence we extend the validity of the conjecture tes(G) = max |E(G)|+2 3 , ∆(G)+1 2 for some more graphs.

Computer Science Review, 2009

Cycles in graphs play an important role in many applications, e.g., analysis of electrical networks, analysis of chemical and biological pathways, periodic scheduling, and graph drawing. From a mathematical point of view, cycles in graphs have a rich structure. Cycle bases are a compact description of the set of all cycles of a graph. In this paper, we survey the state of knowledge on cycle bases and also derive some new results. We introduce different kinds of cycle bases, characterize them in terms of their cycle matrix, and prove structural results and apriori length bounds. We provide polynomial algorithms for the minimum cycle basis problem for some of the classes and prove APX -hardness for others. We also discuss three applications and show that they require different kinds of cycle bases.

International Journal of Computer Applications, 2012

  where N(x) is the set of neighbours of x. f is called a vertex irregular total k-labeling if for every pair of distinct vertices x and y () f wt x  () f wt y. The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G and is denoted by tvs(G). In this paper we find the total vertex irregularity strength of cycle related graphs H(n), DHF(n), F(n,2) and obtain a bound for the total vertex irregularity strength of H graphs H(k).

—Let G be a (p, q) graph. A bijective vertex labeling function f : V (G) → {1, 2,. .. p} is called a difference cordial labeling if for each edge uv, assign the label |f (u) − f (v)| then |e f (0) − e f (1)| ≤ 1, where e f (1) and e f (0) denote the number of edges labeled with 1 and not labeled with 1 respectively. A graph with a difference cordial labeling is called a difference cordial graph. In this paper, we prove that cycle with one chord, cycle with twin chords and cycle with triangle admit difference cordial labeling.

Journal of Algorithms and Computation, 2016

Let G be a (p,q) graph. An injective map f : E(G) → {±1, ±2, • • • , ±q} is said to be an edge pair sum labeling if the induced vertex function f * : V (G) → Z − {0} defined by f * (v) = e Ev f (e) is one-one where E v denotes the set of edges in G that are incident with a vertex v and f * (V (G)) is either of the form ±k 1 , ±k 2 , • • • , ±k p 2 or ±k 1 , ±k 2 , • • • , ±kp−1 2 ±kp+1 2 according as p is even or odd. A graph with an edge pair sum labeling is called an edge pair sum graph. In this paper we prove that the graphs GL(n), double triangular snake D(T n), W n , F l n , C m , K 1,n and C m * K 1,n admit edge pair sum labeling.

Journal of Graph Theory, 2010

We give a structural description of the class C of graphs that do not contain a cycle with a unique chord as an induced subgraph. Our main theorem states that any connected graph in C is a either in some simple basic class or has a decomposition. Basic classes are cliques, bipartite graphs with one side containing only nodes of degree two and induced subgraph of the famous Heawood or Petersen graph. Decompositions are node cutsets consisting of one or two nodes and edge cutsets called 1-joins. Our decomposition theorem actually gives a complete structure theorem for C, i.e. every graph in C can be built from basic graphs that can be explicitly constructed, and gluing them together by prescribed composition operations; and all graphs built this way are in C.