﻿ Line completion number of grid graph Pn × Pm

# Line completion number of grid graph Pn × Pm

##### چکیده

The concept of super line graph was introduced in the year 1995 by Bagga, Beineke and Varma. Given a graph with at least r edges, the super line graph of index r, Lr(G), has as its vertices the sets of r-edges of G, with two adjacent if there is an edge in one set adjacent to an edge in the other set. The line completion number lc(G) of a graph G is the least positive integer r for which Lr(G) is a complete graph. In this paper, we find the line completion number of grid graph Pn × Pm for various cases of n and m.

برای دانلود باید عضویت طلایی داشته باشید

برای دسترسی به متن کامل این مقاله و 10 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

## The Friendly Index Set of Pm × Pn

For a graph G = (V,E) and a binary labeling (coloring) f : V (G) → Z2, let vf (i) = |f−1(i)|. f is said to be friendly if |vf (1) − vf (0)| ≤ 1. The labeling f : V (G) → Z2 induces an edge labeling f∗ : E(G) → Z2 defined by f∗(xy) = |f(x)− f(y)| ∀xy ∈ E(G). Let ef (i) = |f∗−1(i)|. The friendly index set of the graph G, denoted by FI(G), is defined by FI(G) = {|ef (1)− ef (0)| : f is a friendly ...

متن کامل

## The critical groups for Km≚Pn and Pm≚Pn

Let G1∨G2 denote the graph obtained from G1+G2 by adding new edges from each vertex of G1 to every vertex of G2. In this paper, the critical groups of the graphs Km ∨ Pn (n ≥ 4) and Pm ∨ Pn (m ≥ 4, n ≥ 5) are determined.

متن کامل

## A linear algorithm for the Hamiltonian completion number of the line graph of a cactus

Given a graph G = (V; E); HCN (L(G)) is the minimum number of edges to be added to its line graph L(G) to make L(G) Hamiltonian. This problem is known to be NP-hard for general graphs, whereas a O(|V |) algorithm exists when G is a tree. In this paper a linear algorithm for 8nding HCN (L(G)) when G is a cactus is proposed. ? 2003 Elsevier B.V. All rights reserved.

متن کامل

## Uniform Number of a Graph

We introduce the notion of uniform number of a graph. The  uniform number of a connected graph \$G\$ is the least cardinality of a nonempty subset \$M\$ of the vertex set of \$G\$ for which the function \$f_M: M^crightarrow mathcal{P}(X) - {emptyset}\$ defined as \$f_M(x) = {D(x, y): y in M}\$ is a constant function, where \$D(x, y)\$ is the detour distance between \$x\$ and \$y\$ in \$G\$ and \$mathcal{P}(X)\$ ...

متن کامل

## Critical graphs for R(Pn, Pm) and the star-critical Ramsey number for paths

The graph Ramsey number R(G,H) is the smallest integer r such that every 2-coloring of the edges of Kr contains either a red copy of G or a blue copy of H. The star-critical Ramsey number r∗(G,H) is the smallest integer k such that every 2-coloring of the edges of Kr −K1,r−1−k contains either a red copy of G or a blue copy of H. We will classify the critical graphs, 2-colorings of the complete ...

متن کامل

## NEARLY ANTIPODAL CHROMATIC NUMBER ac′(Pn) OF THE PATH Pn

Chartrand et al. (2004) have given an upper bound for the nearly antipodal chromatic number ac′(Pn) as (n−2 2 ) +2 for n > 9 and have found the exact value of ac′(Pn) for n = 5, 6, 7, 8. Here we determine the exact values of ac′(Pn) for n > 8. They are 2p − 6p + 8 for n = 2p and 2p − 4p + 6 for n = 2p + 1. The exact value of the radio antipodal number ac(Pn) for the path Pn of order n has been ...

متن کامل

ذخیره در منابع من

ذخیره شده در منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی راحت تر خواهید کرد

دانلود متن کامل

برای دسترسی به متن کامل این مقاله و 10 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره 6  شماره 2

صفحات  299- 313

تاریخ انتشار 2021-12-01

{@ msg @}

با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.

کلمات کلیدی

میزبانی شده توسط پلتفرم ابری doprax.com