Indicated Coloring of Complete Expansion and Lexicographic Product of Graphs

Another H-super magic decompositions of the lexicographic product of graphs

Indonesian Journal of Combinatorics ◽

10.19184/ijc.2018.2.2.2 ◽

2018 ◽

Vol 2 (2) ◽

pp. 72

Author(s):

H Hendy ◽

Kiki A. Sugeng ◽

A.N.M Salman ◽

Nisa Ayunda

Keyword(s):

Bipartite Graph ◽

Complete Bipartite Graph ◽

Graph Decomposition ◽

Graph Labeling ◽

Sufficient Condition ◽

Lexicographic Product ◽

Simple Graphs ◽

Product Of Graphs

Let H and G be two simple graphs. The concept of an H-magic decomposition of G arises from the combination between graph decomposition and graph labeling. A decomposition of a graph G into isomorphic copies of a graph H is H-magic if there is a bijection f : V(G) ∪ E(G) → {1, 2, ..., ∣V(G) ∪ E(G)∣} such that the sum of labels of edges and vertices of each copy of H in the decomposition is constant. A lexicographic product of two graphs G1 and G2, denoted by G1[G2], is a graph which arises from G1 by replacing each vertex of G1 by a copy of the G2 and each edge of G1 by all edges of the complete bipartite graph Kn, n where n is the order of G2. In this paper we provide a sufficient condition for $\overline{C_{n}}[\overline{K_{m}}]$ in order to have a $P_{t}[\overline{K_{m}}]$-magic decompositions, where n > 3, m > 1, and t = 3, 4, n − 2.

Download Full-text

Doubly connected domination in the corona and lexicographic product of graphs

Applied Mathematical Sciences ◽

10.12988/ams.2014.4136 ◽

2014 ◽

Vol 8 ◽

pp. 1521-1533 ◽

Cited By ~ 1

Author(s):

Benjier H. Arriola ◽

Sergio R. Canoy, Jr.

Keyword(s):

Lexicographic Product ◽

Product Of Graphs

Download Full-text

b -continuity and the lexicographic product of graphs

Electronic Notes in Discrete Mathematics ◽

10.1016/j.endm.2015.07.024 ◽

2015 ◽

Vol 50 ◽

pp. 139-144 ◽

Cited By ~ 2

Author(s):

Cláudia Linhares Sales ◽

Rafael Vargas ◽

Leonardo Sampaio

Keyword(s):

Lexicographic Product ◽

Product Of Graphs

Download Full-text

The geodetic number of the lexicographic product of graphs

Discrete Mathematics ◽

10.1016/j.disc.2011.04.004 ◽

2011 ◽

Vol 311 (16) ◽

pp. 1693-1698 ◽

Cited By ~ 13

Author(s):

Boštjan Brešar ◽

Tadeja Kraner Šumenjak ◽

Aleksandra Tepeh

Keyword(s):

Lexicographic Product ◽

Geodetic Number ◽

Product Of Graphs

Download Full-text

Identifying Codes of Lexicographic Product of Graphs

The Electronic Journal of Combinatorics ◽

10.37236/2974 ◽

2012 ◽

Vol 19 (4) ◽

Cited By ~ 8

Author(s):

Min Feng ◽

Min Xu ◽

Kaishun Wang

Keyword(s):

Connected Graph ◽

Necessary Condition ◽

Lexicographic Product ◽

Arbitrary Graph ◽

Minimum Cardinality ◽

Identifying Codes ◽

Two Parameters ◽

Sufficient And Necessary Condition ◽

Product Of Graphs

Let $G$ be a connected graph and $H$ be an arbitrary graph. In this paper, we study the identifying codes of the lexicographic product $G[H]$ of $G$ and $H$. We first introduce two parameters of $H$, which are closely related to identifying codes of $H$. Then we provide the sufficient and necessary condition for $G[H]$ to be identifiable. Finally, if $G[H]$ is identifiable, we determine the minimum cardinality of identifying codes of $G[H]$ in terms of the order of $G$ and these two parameters of $H$.

Download Full-text

Star coloring under some graph operations

Asian-European Journal of Mathematics ◽

10.1142/s1793557122500796 ◽

2021 ◽

pp. 2250079

Author(s):

B. Akhavan Mahdavi ◽

M. Tavakoli ◽

F. Rahbarnia ◽

Alireza Ashrafi

Keyword(s):

Chromatic Number ◽

Lexicographic Product ◽

Proper Coloring ◽

Sharp Bounds ◽

Graph Operations ◽

Join Of Graphs ◽

Star Coloring ◽

Product Of Graphs

A star coloring of a graph [Formula: see text] is a proper coloring of [Formula: see text] such that no path of length 3 in [Formula: see text] is bicolored. In this paper, the star chromatic number of join of graphs is computed. Some sharp bounds for the star chromatic number of corona, lexicographic, deleted lexicographic and hierarchical product of graphs together with a conjecture on the star chromatic number of lexicographic product of graphs are also presented.

Download Full-text

Helly and exchange numbers of geodesic and Steiner convexities in lexicographic product of graphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830915500494 ◽

2015 ◽

Vol 07 (04) ◽

pp. 1550049 ◽

Cited By ~ 3

Author(s):

Bijo S. Anand ◽

Manoj Changat ◽

Prasanth G. Narasimha-Shenoi

Keyword(s):

Convex Sets ◽

Lexicographic Product ◽

Geodesic Convexity ◽

Induced Path ◽

Arbitrary Graphs ◽

Geodesic Convex ◽

Product Of Graphs ◽

The Way

We discuss the convexity invariants, namely, the exchange and Helly numbers of the Steiner and geodesic convexity in lexicographic product of graphs. We use the structure of both the Steiner and geodesic convex sets in the lexicographic product for proving the results. Along the way the exchange number of the induced path convexity in arbitrary graphs is also determined.

Download Full-text